In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution ... more In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation (with weighted S p-pseudo almost automorphic forcing term) in a Banach space X. We use fractional powers of operators and the Banach fixed point theorem in order to obtain our result. Very recently introduced concept of ''weighted S p-pseudo almost automorphy'' has been used here.
Differential Equations and Dynamical Systems, 2016
In this paper we first consider a linear time invariant systems with almost periodic forcing term... more In this paper we first consider a linear time invariant systems with almost periodic forcing term. We propose a new deterministic quadratic control problem, motivated by Da-Prato. With the help of associated degenerate Riccati equation we study the existence and uniqueness of an almost automorphic solutions.
In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution ... more In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation (with weighted S p-pseudo almost automorphic forcing term) in a Banach space X. We use fractional powers of operators and the Banach fixed point theorem in order to obtain our result. Very recently introduced concept of ''weighted S p-pseudo almost automorphy'' has been used here.
Abstract: In this work we use the theory of evolution semigroup of bounded linear operators and f... more Abstract: In this work we use the theory of evolution semigroup of bounded linear operators and fixed point theorem to establish the existence and uniqueness of a mild solution of a neutral functional differential equation in a Banach space. Keywords: almost automorphic function; evolution semigroup; neutral functional differential equation; mild solution.
In this article, we study the approximate controllability and homegenization results of a semi-li... more In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem.
In this paper we first consider a linear time invariant system with almost automorphic forcing te... more In this paper we first consider a linear time invariant system with almost automorphic forcing term. We propose two new deterministic quadratic control problems motivated by Da-Prato. We make use of a degenerate Riccati equation to solve these control problems. We also study the existence and uniqueness of an almost automorphic solutions of the associated differential equations.
In this paper, we study the L 2 and H 1-approximate controllability and homogenization of a semil... more In this paper, we study the L 2 and H 1-approximate controllability and homogenization of a semilinear elliptic boundary value problem in a perforated domain. The principal term in the state equation has rapidly oscillating coefficients and the control region is free from perforations (holes). The observable zone is locally distributed in the perforation free region, in the case of H 1-approximate controllability. By using the constructive approach introduced by Lions and which is based on the Fenchel-Rockafellar's duality theory, we obtain the approximate control of minimal norm. The existence of the control is established by means of a fixed point argument. Another interesting result of this study is that the minimal norm controls of the ε-problem converge to the optimal controls associated with the homogenized problem. The result in the case of rapidly oscillating coefficients in a fixed domain was proved in [Conca, et al., J. Math. Anal. 285 (2003), 17-36]. The main difficulty relies in passing to the limit in the cost functional (as ε → 0) having rapidly oscillating coefficients.
In this article, we study the asymptotic behavior of solutions to some optimal control problems, ... more In this article, we study the asymptotic behavior of solutions to some optimal control problems, governed by an elliptic boundary value problem with Robin boundary conditions in a periodically perforated domain. The coefficients of the differential operator in the state equation and in the costfunctional are rapidly oscillating. We also study the boundary homogenization of some optimal control problems.
In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution ... more In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation (with weighted S p-pseudo almost automorphic forcing term) in a Banach space X. We use fractional powers of operators and the Banach fixed point theorem in order to obtain our result. Very recently introduced concept of ''weighted S p-pseudo almost automorphy'' has been used here.
Differential Equations and Dynamical Systems, 2016
In this paper we first consider a linear time invariant systems with almost periodic forcing term... more In this paper we first consider a linear time invariant systems with almost periodic forcing term. We propose a new deterministic quadratic control problem, motivated by Da-Prato. With the help of associated degenerate Riccati equation we study the existence and uniqueness of an almost automorphic solutions.
In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution ... more In this paper, we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation (with weighted S p-pseudo almost automorphic forcing term) in a Banach space X. We use fractional powers of operators and the Banach fixed point theorem in order to obtain our result. Very recently introduced concept of ''weighted S p-pseudo almost automorphy'' has been used here.
Abstract: In this work we use the theory of evolution semigroup of bounded linear operators and f... more Abstract: In this work we use the theory of evolution semigroup of bounded linear operators and fixed point theorem to establish the existence and uniqueness of a mild solution of a neutral functional differential equation in a Banach space. Keywords: almost automorphic function; evolution semigroup; neutral functional differential equation; mild solution.
In this article, we study the approximate controllability and homegenization results of a semi-li... more In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem.
In this paper we first consider a linear time invariant system with almost automorphic forcing te... more In this paper we first consider a linear time invariant system with almost automorphic forcing term. We propose two new deterministic quadratic control problems motivated by Da-Prato. We make use of a degenerate Riccati equation to solve these control problems. We also study the existence and uniqueness of an almost automorphic solutions of the associated differential equations.
In this paper, we study the L 2 and H 1-approximate controllability and homogenization of a semil... more In this paper, we study the L 2 and H 1-approximate controllability and homogenization of a semilinear elliptic boundary value problem in a perforated domain. The principal term in the state equation has rapidly oscillating coefficients and the control region is free from perforations (holes). The observable zone is locally distributed in the perforation free region, in the case of H 1-approximate controllability. By using the constructive approach introduced by Lions and which is based on the Fenchel-Rockafellar's duality theory, we obtain the approximate control of minimal norm. The existence of the control is established by means of a fixed point argument. Another interesting result of this study is that the minimal norm controls of the ε-problem converge to the optimal controls associated with the homogenized problem. The result in the case of rapidly oscillating coefficients in a fixed domain was proved in [Conca, et al., J. Math. Anal. 285 (2003), 17-36]. The main difficulty relies in passing to the limit in the cost functional (as ε → 0) having rapidly oscillating coefficients.
In this article, we study the asymptotic behavior of solutions to some optimal control problems, ... more In this article, we study the asymptotic behavior of solutions to some optimal control problems, governed by an elliptic boundary value problem with Robin boundary conditions in a periodically perforated domain. The coefficients of the differential operator in the state equation and in the costfunctional are rapidly oscillating. We also study the boundary homogenization of some optimal control problems.
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