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Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition

  • A. K. NandakumaranEmail author
  • M. Rajesh
Article

Abstract

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, Ωɛ = ΩS ε is a periodically perforated domain andd ε is a sequence of positive numbers which goes to zero. We obtain the homogenized equation. The homogenization of the equations on a fixed domain and also the case of perforated domain with Neumann boundary condition was studied by the authors. The homogenization for a fixed domain and\(b(\frac{x}{{d_\varepsilon }},u_\varepsilon ) \equiv b(u_\varepsilon )\) has been done by Jian. We also obtain certain corrector results to improve the weak convergence.

Keywords

Homogenization perforated domain correctors 

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Copyright information

© Indian Academy of Sciences 2002

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.ANLA, U.F.R. des Sciences et TechniquesUniversité de Toulon et du VarLa Garde CedexFrance

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