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

Authors:

A. K. Nandakumaran M. Rajesh

Affiliation:

(1) Department of Mathematics, Indian Institute of Science, 560 012 Bangalore, India

Abstract:

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains

$begin{gathered} partial _t b(tfrac{x}{varepsilon },u_varepsilon ) - diva(tfrac{x}{varepsilon },u_varepsilon ,nabla u_varepsilon ) = f(x,t) in Omega _varepsilon times (0,T), hfill a(tfrac{x}{varepsilon },u_varepsilon ,nabla u_varepsilon ) cdot v_varepsilon = 0 on partial S_varepsilon times (0,T), hfill u_varepsilon = 0 on partial Omega times (0,T), hfill u_varepsilon (x,0) = u_0 (x) in Omega _varepsilon hfill end{gathered}$

. Here, Ω_ɛ=ΩS _ɛ is a periodically perforated domain. We obtain the homogenized equation and corrector results. The homogenization of the equations on a fixed domain was studied by the authors [15]. The homogenization for a fixed domain and $b(tfrac{x}{varepsilon },u_varepsilon ) equiv b(u_varepsilon )$ has been done by Jian [11].

Keywords:

Homogenization perforated domain two-scale convergence correctors

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