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

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/112/03/0425-0439

    • Keywords

       

      Homogenization; perforated domain; correctors

    • 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= ΩSε is a periodically perforated domain anddε 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.

    • Author Affiliations

       

      A K Nandakumaran1 M Rajesh2

      1. Department of Mathematics, Indian Institute of Science, Bangalore - 560 012, India
      2. ANLA, U.F.R. des Sciences et Techniques, Université de Toulon et du Var, BP 132, La Garde Cedex - 83957, France
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.