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.
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|
|Additional Information:||Copyright for this article belongs to Indian Academy of Sciences.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||22 Sep 2004|
|Last Modified:||19 Sep 2010 04:16|
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