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

Nandakumaran, AK and Rajesh, M (2002) Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition. In: Proceedings of the Indian Academy of Sciences Mathematical Sciences, 112 (3). pp. 425-439.

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Abstract

In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains a,b (x/d(e), u(epsilon)) - div a(u(epsilon), delu(epsilon)) = f(x, t) in Omega(epsilon) x (0, T), u(epsilon) = 0 on partial derivativeOmega(epsilon) x (0, T), u(epsilon) (x, 0) = u(0)(x) in Omega(epsilon). Here, Omega(epsilon) = Omega S-epsilon is a periodically perforated domain and d(epsilon) 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(x/d(epsilon), u(epsilon)) = b(u(epsilon)) has been done bit Jian. We also obtain certain corrector results to improve the weak convergence.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences Mathematical Sciences
Publisher:	Indian Academy Sciences
Additional Information:	Copyright for this article belongs to Indian Academy of Sciences.
Keywords:	Homogenization;perforated domain;correctors
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	22 Sep 2004
Last Modified:	19 Sep 2010 04:16
URI:	http://eprints.iisc.ac.in/id/eprint/2002

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