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. 425439.

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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 Sepsilon 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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