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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:
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 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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
Three methods for the study of semilinear equations at resonance
Autorzy:
Przeradzki, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/967213.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.
Źródło:
Colloquium Mathematicum; 1993, 66, 1; 109-12
0010-1354
Pojawia się w:
Colloquium Mathematicum
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:
Existence of periodic solutions for semilinear parabolic equations
Autorzy:
Hirano, Norimichi
Mizoguchi, Noriko
Powiązania:
https://bibliotekanauki.pl/articles/1358924.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if $(t,x) ∈ R_{+} × Ω$ u = 0 if $(t,x) ∈ R_{+} × ∂Ω$, where $Ω ⊂ R^{N}$ is a bounded domain with smooth boundary ∂Ω and $g : R _{+} × \bar{Ω} × R → R $ is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.
Źródło:
Banach Center Publications; 1996, 35, 1; 39-49
0137-6934
Pojawia się w:
Banach Center Publications
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:
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:
Semilinear relations and *-representations of deformations of so(3)
Autorzy:
Samoĭlenko, Yuriĭ
Turowska, Lyudmila
Powiązania:
https://bibliotekanauki.pl/articles/1342700.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
We study a family of commuting selfadjoint operators $=(A_k)_{k=1}^n$, which satisfy, together with the operators of the family $=(B_j)_{j=1}^{n}$, semilinear relations $⅀ _{i} f_{ij}() B_j g_{ij}() = h()$, ($f_{ij}$, $g_{ij}$, $h_j: ℝ^n → ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_q'(so(3))$.
Źródło:
Banach Center Publications; 1997, 40, 1; 21-40
0137-6934
Pojawia się w:
Banach Center Publications
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:
Review: Entire solutions of semilinear elliptic equations by I. Kuzin, S. Pohozaev
Autorzy:
Kołakowski, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/748174.pdf
Data publikacji:
1999
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
.
Opis:
Artykuł nie zawiera streszczenia
The article contains no abstract
Źródło:
Mathematica Applicanda; 1999, 27, 41
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference schemes of arbitrary order of accuracy for semilinear parabolic equations
Autorzy:
Lapinska-Chrzczonowicz, Magdalena
Powiązania:
https://bibliotekanauki.pl/articles/764477.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Źródło:
Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica; 2010, 10, 2
1732-1360
2083-3628
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
Local Controllability of Fractional Discrete-Time Semilinear Systems
Autorzy:
Klamka, J.
Powiązania:
https://bibliotekanauki.pl/articles/387282.pdf
Data publikacji:
2011
Wydawca:
Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
Tematy:
sterowanie
możliwość kontroli
discrete-time systems
controllability
Opis:
In the paper unconstrained local controllability problem of finite-dimensional fractional discrete-time semilinear systems with constant coefficients is addressed. Using general formula of solution of difference state equation sufficient condition for local unconstrained controllability in a given number of steps is formulated and proved. Simple illustrative example is also presented.
Źródło:
Acta Mechanica et Automatica; 2011, 5, 2; 55-58
1898-4088
2300-5319
Pojawia się w:
Acta Mechanica et Automatica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pseudospectral method for semilinear partial functional differential equations
Autorzy:
Czernous, W.
Powiązania:
https://bibliotekanauki.pl/articles/255893.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
pseudospectral collocation
CFS condition
convergence
error estimates
Opis:
We present a convergence result for two spectral methods applied to an initial boundary value problem with functional dependence of Volterra type. Explicit condition of Courant-Friedrichs-Levy type is assumed on time step τ and the number N of collocation points. Stability statements and error estimates are written using continuous norms in weighted Jacobi spaces.
Źródło:
Opuscula Mathematica; 2010, 30, 2; 133-145
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis
Autorzy:
Jais, M.
Powiązania:
https://bibliotekanauki.pl/articles/255103.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
hysteresis
parabolic
inverse problem
uniqueness
Opis:
We consider the solvability of the semilinear parabolic differential equation [formula] in a cylinder D = Ω x (0, T), where Ρ is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach operator Ρ from overdetermined boundary data.
Źródło:
Opuscula Mathematica; 2008, 28, 1; 47-62
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
Autorzy:
Levine, Howard
Powiązania:
https://bibliotekanauki.pl/articles/1359469.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Banach Center Publications; 1996, 33, 1; 193-198
0137-6934
Pojawia się w:
Banach Center Publications
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:
A note on solutions of semilinear equations at resonance in a cone
Autorzy:
Przeradzki, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/1311896.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonnegative solutions
equations at resonance
Opis:
A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).
Źródło:
Annales Polonici Mathematici; 1993, 58, 1; 95-103
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities
Autorzy:
Zuazua, E.
Powiązania:
https://bibliotekanauki.pl/articles/206681.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
controllability
nolinear PDEs of parabolic type
systems governed by PDFs
Opis:
We consider the semilinear heat equation involving gradient terms in a bounded domain of [R^n]. It is assumed that the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when t1e control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the contool may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints.
Źródło:
Control and Cybernetics; 1999, 28, 3; 665-683
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Parametric Borel summability for some semilinear system of partial differential equations
Autorzy:
Yamazawa, H.
Yoshino, M.
Powiązania:
https://bibliotekanauki.pl/articles/254935.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Borel summability
singular perturbation
Euler type operator
Opis:
In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with n independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
Źródło:
Opuscula Mathematica; 2015, 35, 5; 825-845
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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
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