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Wyświetlanie 1-15 z 41
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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
Wyświetlanie 1-15 z 41

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