M Rajesh
Articles written in Proceedings – Mathematical Sciences
Volume 108 Issue 2 June 1998 pp 189-207
Homogenization of periodic optimal control problems via multi-scale convergence
The aim of this paper is to provide an alternate treatment of the homogenization of an optimal control problem in the framework of two-scale (multi-scale) convergence in the periodic case. The main advantage of this method is that we are able to show the convergence of cost functionals directly without going through the adjoint equation. We use a corrector result for the solution of the state equation to achieve this.
Volume 112 Issue 1 February 2002 pp 195-207
Homogenization of a parabolic equation in perforated domain with Neumann boundary condition
In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains$$\begin{gathered} \partial _t b(\tfrac{x}{\varepsilon },u_\varepsilon ) - diva(\tfrac{x}{\varepsilon },u_\varepsilon ,\nabla u_\varepsilon ) = f(x,t) in \Omega _\varepsilon \times (0,T), \hfill \\ a(\tfrac{x}{\varepsilon },u_\varepsilon ,\nabla u_\varepsilon ) \cdot v_\varepsilon = 0 on \partial S_\varepsilon \times (0,T), \hfill \\ u_\varepsilon = 0 on \partial \Omega \times (0,T), \hfill \\ u_\varepsilon (x,0) = u_0 (x) in \Omega _\varepsilon \hfill \\ \end{gathered} $$. Here, Ω_{ɛ}=Ω
Volume 112 Issue 2 May 2002 pp 337-346
On the limit matrix obtained in the homogenization of an optimal control problem
A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices).
Volume 112 Issue 3 August 2002 pp 425-439
Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition
In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains$$\begin{gathered} \partial _t b(\tfrac{x}{{d_\varepsilon }},u_\varepsilon ) - div a(u_\varepsilon , \nabla u_\varepsilon ) = f(x,t) in \Omega _\varepsilon x (0, T), \hfill \\ u_\varepsilon ) = 0 on \partial \Omega _\varepsilon x (0, T), \hfill \\ u_\varepsilon (x, 0) = u_0 (x) in \Omega _\varepsilon . \hfill \\ \end{gathered} $$. Here, Ω_{ɛ}
Volume 133, 2023
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