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    Wyświetlanie 1-6 z 6
    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:
    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:
    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:
    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:
    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:
    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
      Wyświetlanie 1-6 z 6

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