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    Wyświetlanie 1-41 z 41
    Tytuł:
    Controllability of semilinear wave equations with infinitely iterated logarithms
    Autorzy:
    Cannarsa, P.
    Komornik, V.
    Loreti, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/206588.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    controllability
    semilinear equation
    wave equation
    Opis:
    In a previous work we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua, on the boundary exact controllability of semilinear wave equations by weakening the growth assumptions on the nonlinearity. Answering a question of Zuazua we give a still weaker, essentially optimal condition. Furthermore, we establish an approximate internal controllability result under the same growth assumptions.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 449-461
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Second order semilinear Volterra integrodifferential equation in Banach space
    Autorzy:
    Bochenek, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1311971.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    cosine family
    semilinear Volterra equation
    Opis:
    By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
    Źródło:
    Annales Polonici Mathematici; 1992, 57, 3; 231-241
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On periodic oscillations for a class of feedback control systems in Hilbert spaces
    Autorzy:
    Loi, Nguyen
    Powiązania:
    https://bibliotekanauki.pl/articles/729532.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear differential inclusion
    periodic solution
    guiding function
    Opis:
    In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 205-219
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of a model of combined anticancer therapy
    Autorzy:
    Klamka, J.
    Świerniak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/206596.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    controllability
    semilinear systems
    biomathematical modelling
    cancer therapy
    Opis:
    Controllability of combination of antiangiogenic treatment and chemotherapy is considered. A model used in the paper is a finite-dimensional dynamical control system described by secondo order semilinear time invariant ordinary differential state equations. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear second-order dynamical control system.
    Źródło:
    Control and Cybernetics; 2013, 42, 1; 123-138
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
    Autorzy:
    Maslowski, B.
    Simão, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/966652.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    invariant measures
    mixing
    stochastic semilinear equations
    ergodicity
    Źródło:
    Colloquium Mathematicum; 1997, 72, 1; 147-171
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A viability result for nonconvex semilinear functional differential inclusions
    Autorzy:
    Lupulescu, Vasile
    Necula, Mihai
    Powiązania:
    https://bibliotekanauki.pl/articles/729593.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    viability
    invariance
    tangency condition
    semilinear differential inclusions
    Opis:
    We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 109-128
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence theorems for a semilinear elliptic boundary value problem
    Autorzy:
    Marano, Salvatore
    Powiązania:
    https://bibliotekanauki.pl/articles/1311657.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    elliptic differential inclusions
    semilinear elliptic equations
    strong solutions
    Opis:
    Let Ω be a bounded domain in $ℝ^n$, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem { f(x,u) ≤ Lu ≤ g(x,u)   in Ω, u = 0     on ∂Ω, has at least one strong solution $u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.
    Źródło:
    Annales Polonici Mathematici; 1994-1995, 60, 1; 57-67
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1 nonlinearity
    Autorzy:
    Ahmad Ali, Ahmad
    Deckelnick, Klaus
    Hinze, Michael
    Powiązania:
    https://bibliotekanauki.pl/articles/1839143.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    semilinear PDE
    uniqueness of global solutions
    Opis:
    We consider a semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work, presented in Ahmad Ali, Deckelnick and Hinze (2016) we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by G¨unter Leugering, who raised the question whether the problem class considered in Ahmad Ali, Deckelnick and Hinze (2016) can be extended to the nonlinearity φ(s) = s|s|. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice.
    Źródło:
    Control and Cybernetics; 2019, 48, 2; 325-344
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
    Autorzy:
    Nakao, Mitsuhiro
    Powiązania:
    https://bibliotekanauki.pl/articles/1397374.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    energy decay
    global existence
    semilinear wave equation
    noncylindrical domains
    Opis:
    We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain $\cup_{0 \leq t \leq \infty} \Omega(t) \times \{t\} \subset \mathbb{R}^N \times \mathbb{R}$. We are interested in finite energy solution. We derive an exponential decay of the energy in the case Ω(t) is bounded in $\mathbb{R}^N$ and the estimate $\int_0^\infty E(t)dt \leq C(E(0), ||u(0)||) < \infty $ in the case Ω (t) is unbounded. Existence and uniqueness of finite energy solution are also proved.
    Źródło:
    Opuscula Mathematica; 2020, 40, 6; 725-736
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions
    Autorzy:
    Krug, Richard
    Leugering, Günter
    Martin, Alexander
    Schmidt, Martin
    Weninger, Dieter
    Powiązania:
    https://bibliotekanauki.pl/articles/2183473.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    time-domain decomposition
    optimal control
    semilinear hyperbolic systems
    convergence
    Opis:
    In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.
    Źródło:
    Control and Cybernetics; 2021, 50, 4; 427--455
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact controllability for the semilinear string equation in non cylindrical domains
    Autorzy:
    Araruna, F. D.
    Antunes, G. O.
    Medeiros, L. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/970361.pdf
    Data publikacji:
    2004
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowność
    półliniowość
    exact controllability
    string equation
    semilinear
    non cylindrical
    Opis:
    In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).
    Źródło:
    Control and Cybernetics; 2004, 33, 2; 237-257
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate Controllability Properties of the Semilinear Heat Equation With Lumped Controls
    Autorzy:
    Khapalov, A. Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/908269.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowność
    sterowanie skupione
    semilinear heat equation
    controllability
    internal lumped control
    Opis:
    In this article, we study the global controllability properties of aone-dimensional semilinear heat equation with sublinear reaction term, governed in a bounded domain by internal lumped controls. We prove thatit is possible to exactly control any finite dimensional portion of its solution (when expanded along the sequence of the eigenfunctions of the associated Laplacian), provided that the truncated linear equationis approximately controllable in L^2 (0,1). We also describe a certain topology (weaker than L^2 (0,1)) in which this system is, in fact, globally approximately controllable at any positive time. Some extensions to the case of several dimensions are also given.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 1999, 9, 4; 751-765
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Semilinear evolution equations of the parabolic type
    Autorzy:
    Bochenek, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1293838.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    classical solution
    semilinear initial value problem
    analytic semigroup
    mild solution
    Opis:
    This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
    Źródło:
    Annales Polonici Mathematici; 1999, 72, 3; 197-206
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain
    Autorzy:
    Chaieb, M.
    Dhifli, A.
    Zermani, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/256009.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    semilinear elliptic system
    asymptotic behavior
    Karamata class
    sub-super solution
    Opis:
    Let Ω be a bounded domain in [formula] with a smooth boundary [formula]. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system [formula] Here r, s ∈ R, α, β < 1 such that γ := (1 - α) (1 - β ) - rs > 0 and the functions [formula] are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.
    Źródło:
    Opuscula Mathematica; 2016, 36, 3; 315-336
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An abstract semilinear first order differential equation in the hyperbolic case
    Autorzy:
    Bochenek, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/1311559.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    semilinear initial value problem
    stable family of operators
    hyperbolic case
    Opis:
    This paper is devoted to the investigation of the abstract semilinear initial value problem $du/dt = A(t)u + f(t,u), u(0) = u_0$, in the "hyperbolic" case.
    Źródło:
    Annales Polonici Mathematici; 1995, 61, 1; 13-23
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas flow in networks
    Autorzy:
    Leugering, G.
    Martin, A.
    Schmidt, M.
    Sirvent, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/205527.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    gas networks
    Euler equation
    semilinear PDE
    nonoverlapping domain decomposition
    Opis:
    We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.
    Źródło:
    Control and Cybernetics; 2017, 46, 3; 191-225
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal sparse boundary control for a semilinear parabolic equation with mixed control-state constraints
    Autorzy:
    Casas, Eduardo
    Troltzsch, Fredi
    Powiązania:
    https://bibliotekanauki.pl/articles/970122.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    semilinear parabolic equation
    optimal control
    sparse boundary control
    mixed control-state constraints
    Opis:
    A problem of sparse optimal boundary control for a semilinear parabolic partial differential equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic objective functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Applying a recent linearization theorem, we derive first-order necessary optimality conditions in terms of a variational inequality under linearized mixed control state constraints. Based on this preliminary result, a Lagrange multiplier rule with bounded and measurable multipliers is derived and sparsity results on the optimal control are demonstrated.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 89-124
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new composition theorem for sp-weighted pseudo almost periodic functions and applications to semilinear differential equations
    Autorzy:
    Zhao, Z.
    Chang, Y.
    N'Guerekata, G. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/256044.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Sp-weighted pseudo almost periodic
    weighted pseudo almost periodicity
    semilinear differential equations
    Opis:
    In this paper, we establish a new composition theorem for Sp-weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 457-474
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constrained controllability of second order dynami cal systems with delay
    Autorzy:
    Klamka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/205540.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    controllability
    second-order dynamical systems
    delayed control systems
    semilinear control systems
    constrained controls
    Opis:
    The paper considers finite-dimensional dynami cal control systems described by second order semilinear stationary ordinary differential state equations with delay in control. Using a generalized open mapping theorem, sufficient conditions for constrained local controllability in a given time interval are formulated and proved. These conditions require verification of constrained global controllability of the associated linear first-order dynamical control system. It is generally assumed that the values of admissible controls are in a convex and closed cone with vertex at zero. Moreover, several remarks and comments on the existing results for controllability of semilinear dynamical control systems are also presented. Finally, a simple numerical example which illustrates theoretical considerations is also given. It should be pointed out that the results given in the paper extend for the case of semilinear second-order dynamical systems constrained controllability conditions, which were previously known only for linear second-order systems.
    Źródło:
    Control and Cybernetics; 2013, 42, 1; 111-121
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Second-order optimality conditions for semilinear elliptic control problems with constraints on the gradient of the state
    Autorzy:
    Casas, E.
    Fernandez, J.
    Mateos, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206719.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    optimal control
    second order conditions
    semilinear elliptic PDE
    state gradient constraints
    Opis:
    The aim of this paper is to state the second order necessary and sufficient optimality conditions for distributed control problems governed by the Neumann problem associated to a semilinear elliptic partial differential equation. Bound constraints ou control are considered, as well as equality and inequality constraints of integral type on the gradient of the state.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 463-479
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations
    Autorzy:
    Maksimov, Vyacheslav
    Trlötzsch, Fredi
    Powiązania:
    https://bibliotekanauki.pl/articles/329903.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    semilinear parabolic equation
    input reconstruction
    feedback control
    równanie paraboliczne
    równanie semiliniowe
    sprzężenie zwrotne
    Opis:
    Dynamical reconstruction of unknown time-varying controls from inexact measurements of the state function is investigated for a semilinear parabolic equation with memory. This system includes as particular cases the Schlögl model and the FitzHugh–Nagumo equations. A numerical method is suggested that is based on techniques of feedback control. An error analysis is performed. Numerical examples confirm the theoretical predictions.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 5-22
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a semilinear elliptic eigenvalue problem
    Autorzy:
    Coclite, Mario
    Powiązania:
    https://bibliotekanauki.pl/articles/1294623.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    semilinear elliptic equations
    nonlinear boundary-value problems
    positive solutions
    supersolution and subsolution method
    Opis:
    We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_{∂Ω} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.
    Źródło:
    Annales Polonici Mathematici; 1997, 67, 3; 289-295
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces
    Autorzy:
    Abada, Nadjat
    Benchohra, Mouffak
    Hammouche, Hadda
    Ouahab, Abdelghani
    Powiązania:
    https://bibliotekanauki.pl/articles/729413.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear functional differential inclusions
    impulses
    mild solution
    fixed point
    controllability
    extrapolation space
    nondensely defined operator
    Opis:
    In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 329-347
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact determinantions of maximal output admissible set for a class of semilinear discrete systems
    Autorzy:
    El Bhih, Amine
    Benfatah, Youssef
    Rachik, Mostafa
    Powiązania:
    https://bibliotekanauki.pl/articles/229674.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    discrete-time
    output admissible set
    semilinear system
    asymptotic stability
    uncontrolled system
    controlled system
    delayed system
    Opis:
    Consider the semilinear system defined by {x(i+1)=Ax(i)+f(x(i)), i≥0 x(0)=x0∈Rn and the corresponding output signal y(i)=C x(i), i≥0, where A is a n×n matrix, C is a p x n matrix and f is a nonlinear function. An initial state x(0) is output admissible with respect to A, f, C and a constraint set Ω ⊂ Rp, if the output signal (y(i)i associated to our system satisfies the condition y(i) ∈ Ω, for every integer i≥0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems(controlled and uncontrolled systems) .Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.
    Źródło:
    Archives of Control Sciences; 2020, 30, 3; 523-552
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
    Autorzy:
    Zabawa, T.S.
    Powiązania:
    https://bibliotekanauki.pl/articles/254967.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    stability of solutions
    infinite systems
    parabolic equations
    elliptic equations
    semilinear differential-functional equations
    monotone iteration method
    Opis:
    A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
    Źródło:
    Opuscula Mathematica; 2006, 26, 1; 173-183
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and controllability results for semilinear neutral functional differential inclusions with nonlocal conditions
    Autorzy:
    Ntouyas, S.
    O'Regan, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/729421.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    semilinear differential inclusions
    nonlocal conditions
    analytic semigroups
    cosine functions
    integrated semigroups
    fixed point
    nonlinear alternative
    controllability
    Opis:
    In this paper, we prove existence and controllability results for first and second order semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces, with nonlocal conditions. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 213-264
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact penalization of pointwise constraints for optimal control problems
    Autorzy:
    Casas, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/970884.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    semilinear elliptic equations
    pointwise state constraints
    exact penalization
    first and second order optimality conditions
    Opis:
    In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.
    Źródło:
    Control and Cybernetics; 2009, 38, 4A; 1131-1150
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay
    Autorzy:
    Benchohra, Mouffak
    Bennihi, Omar
    Ezzinbi, Khalil
    Powiązania:
    https://bibliotekanauki.pl/articles/746657.pdf
    Data publikacji:
    2013
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    semilinear functional differential equation, mild solution, resolvent family, fixed point, state-dependent delay, contractive map, Frechet space
    Opis:
    In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon-Granas type for contractions maps in Frechet spaces combined with \(\alpha\)-resolvent family is the main tool in our analysis.
    Źródło:
    Commentationes Mathematicae; 2013, 53, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions
    Autorzy:
    Cabada, Dalia
    Garcia, Katherine
    Guevara, Cristi
    Leiva, Hugo
    Powiązania:
    https://bibliotekanauki.pl/articles/2134894.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    exact controllability
    semilinear time varying control systems
    non-instantaneous impulses
    delay
    nonlocal conditions
    Rothe's fixed point theorem
    Opis:
    In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.
    Źródło:
    Archives of Control Sciences; 2022, 32, 2; 335--357
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An existence result for impulsive functional differential inclusions in Banach spaces
    Autorzy:
    Benedetti, Irene
    Powiązania:
    https://bibliotekanauki.pl/articles/729505.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    impulsive functional differential inclusion
    semilinear differential inclusion
    mild solution
    Cauchy problem
    solution set
    condensing multimap
    fixed point
    Opis:
    We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 13-30
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints
    Autorzy:
    Neitzel, I.
    Troltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/970314.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    semilinear parabolic equation
    pointwise state constraints
    Moreau-Yosida regularization
    Lavrentiev regularization
    convergence
    strong regularity
    local uniqueness
    Opis:
    Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence of global and local solutions is addressed. Moreover, strong regularity of the Lavrentiev-regularized optimality system is shown under certain assumptions, which, in particular, allows to show that locally optimal solutions of the Lavrentiev regularized problems are locally unique. This analysis is based on a second-order sufficient optimality condition and a separation assumption on almost active sets.
    Źródło:
    Control and Cybernetics; 2008, 37, 4; 1013-1043
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
    Autorzy:
    Sikora, Beata
    Powiązania:
    https://bibliotekanauki.pl/articles/27312002.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    Hilfer fractional derivative
    fractional systems
    semilinear control systems
    nonautonomous systems
    Rothe's fixed point theorem
    generalized Darbo fixed point theorem
    Opis:
    In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function f depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 155--178
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On controllability of second order dynamical systems – a survey
    Autorzy:
    Klamka, J.
    Wyrwał, J.
    Zawiski, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/202359.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    exact controllability
    approximate controllability
    second-order dynamical systems
    infinite dimensional systems
    semilinear systems
    sterowalność
    układ nieskończenie wymiarowy
    system półliniowy
    Opis:
    The paper presents a survey of recent results in the area of controllability of second order dynamical systems. Controllability problem for finite and infinite dimensional, linear, semilinear, deterministic and stochastic dynamical systems (with delays and undelayed) is taken into consideration. Different types of controllability are discussed.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 3; 279-295
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error estimates for the finite-element approximation of a semilinear elliptic control problem
    Autorzy:
    Casas, E.
    Troeltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/206743.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja numeryczna
    metoda elementu skończonego
    równanie eliptyczne półliniowe
    sterowanie rozproszone
    distributed control
    error estimates
    finite element method
    numerical approximation
    semilinear elliptic equation
    Opis:
    We consider the finite-element approximation of a distributed optimal control problem governed by a semilinear elliptic partial differential equation, where pointwise constraints on the control are given. We prove the existence of local approximate solutions converging to a given local reference solution. Moreover, we derive error estimates for local solutions in the maximum norm.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 695-712
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
    Autorzy:
    Brzychczy, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255097.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    infinite systems
    reaction-diffusion-convection equations
    semilinear parabolic differential-functional equations
    Volterra functionals
    monotone iterative methods
    method of upper and lower solutions
    Opis:
    We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 29-99
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An output controllability problem for semilinear distributed hyperbolic systems
    Autorzy:
    Zerrik, E.
    Larhrissi, R.
    Bourray, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/929815.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system o parametrach rozłożonych
    system półliniowy
    system hyperboliczny
    sterowność wymuszona
    punkt stały
    distributed-parameter systems
    semilinear hyperbolic systems
    constrained controllability
    fixed point
    Opis:
    The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 4; 437-446
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate controllability of the impulsive semilinear heat equation
    Autorzy:
    Leiva, H.
    Merentes, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/357798.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    impulsive semilinear heat equation
    approximate controllability
    Rothe's fixed point theorem
    functional analysis
    teoria punktu stałego
    przestrzeń Banacha
    równanie przewodnictwa ciepła
    sterowalność
    analiza funkcjonalna
    Opis:
    In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation \[ \begin{cases} z_{t} = \Delta z + 1_{\omega}u(t,x) + f(t,z,u(t,x)), & \text{in} \quad (0,\tau] \times \Omega, t \neq t_{k}) \\ z = 0, & \text{on} \quad (0, \tau) \times \delta\Omega,\\ z(0,x) = z_{0}(x), & x \in \Omega, \\ z(t_{k}^{+}, x) = z(t_{k}^{-}, x) + I_{k}(t_{k},z(t_{k},x)u(t_{k},x)), & x \in \Omega, \end{cases} \] where k = 1, 2, . . . , p, $\Omega$ is a bounded domain in $\mathbb{R}^{N}(N \geq 1), z_{0} \in L_{2}(\Omega), \omega$ is an open nonempty subset of $\Omega$, $1_{\omega}$ denotes the characteristic function of the set $\omega$, the distributed control $u$ belongs to $C\left([0, \tau]; L_{2}\left(\Omega\right)\right)$ and $f,I_{k} \in C([0, \tau] \times \mathbb{R} \times \mathbb{R}; \mathbb{R}), k = 1, 2, 3, \ldots, p$, such that \[ |f(t,z,u)| \leq a_{0}|z|^{\alpha_{0}} + b_{0}|u|^{\beta_{0}} +c_{0}, \quad u \in \mathbb{R}, z \in \mathbb{R}. \] \[ |I_{k}(t,z,u)| \leq a_{k}|z|^{\alpha_{k}} + b_{k}|u|^{\beta_{k}} +c_{k}, k=1,2,3 \ldots, pu \in \mathbb{R}, z \in \mathbb{R} \] with $\frac{1}{2} \leq \alpha_{k} < 1, \frac{1}{2} \leq \beta_{k} < 1, k= 0,1,2,3, \ldots, p$ Under this condition we prove the following statement: For all open nonempty subsets $\omega$ of $\Omega$ the system is approximately controllable on $[0, \tau]$. Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state $z_{0}$ to an $\epsilon$ neighborhood of the nal state $z_{1}$ at time $\tau > 0$.
    Źródło:
    Journal of Mathematics and Applications; 2015, 38; 85-104
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control of semilinear evolution inclusions via discrete approximations
    Autorzy:
    Mordukhovich, B. S.
    Wang, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839178.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    analiza wariacyjna
    różniczkowanie uogólnione
    aproksymacja dyskretna
    warunek konieczny optymalności
    optimal control
    variational analysis
    generalized differentiation
    semilinear evolution inclusions
    discrete approximations
    necessary optimality conditions
    Opis:
    This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.
    Źródło:
    Control and Cybernetics; 2005, 34, 3; 849-870
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Discrete relaxed method for semilinear parabolic optimal control problem
    Autorzy:
    Chryssoverghi, I.
    Coletsos, J.
    Kokkinis, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/205973.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sterowanie optymalne
    accumulation points
    discrete optimisation method
    discretization
    distributed control
    minimum principle
    optimal control
    parabolic equations
    partial differential equations
    penalty method
    relaxed control
    semilinear parabolic system
    Opis:
    We consider an optimal control problem for systems governed by semilinear parabolic partial differential equations with control and state constraints, without any convexity assumptions. A discrete optimization method is proposed to solve this problem in its relaxed form which combines a penalized Armijo type method with a finite element discretization and constructs sequences of discrete Gamkrelidze relaxed controls. Under appropriate assumptions, we prove that accumulation points of these sequences satisfy the relaxed Pontryagin necessary conditions for optimality. Moreover, we show that the Gamkrelidze controls thus generated can be replaced by simulating piecewise constant classical controls.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 157-176
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Sequential optimization for semilinear divergent hyperbolic equation with a boundary control and state inequality constraint
    Autorzy:
    Gavrilov, V. S.
    Sumin, M. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/206311.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Radon measures
    sequential optimization
    maximum principle for minimizing sequences
    semilinear hyperbolic partial differential equations
    pointwise in time state constraints
    boundary control
    value function
    sensitivity
    normality
    regularity
    twoparameter needle variation of controls
    Opis:
    An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.
    Źródło:
    Control and Cybernetics; 2014, 43, 2; 183-226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence of Tolands critical points for sequences of D.C. functions and application to the resolution of semilinear elliptic problems
    Autorzy:
    Yassine, A.
    Alaa, N.
    Elhilali Alaoui, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/206580.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    algorytm proksymalny
    funkcje D.C.
    optymalizacja niewypukła
    punkt krytyczny Tolanda
    semiliniowe zagadnienie eliptyczne
    dc functions
    non-convex optimization
    normalized D.C. decomposition
    proximal algorithm
    semilinear elliptic problem
    Toland's critical point
    Opis:
    We prove that if a sequence (fn)n of D.C. functions (Difference of two Convex functions) converges to a D.C. function f in some appropriate way and if un is a critical point of fn, in the sense described by Toland, and is such that (un)n converges to u, then a is a critical point of f, still in Toland's sense. We also build a new algorithm which searches for this critical point u and then apply it in order to compute the solution of a semilinear elliptic equation.
    Źródło:
    Control and Cybernetics; 2001, 30, 4; 405-417
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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