Homogenized model of reaction-diffusion in a porous medium

We study the initial boundary value problem for the reaction-diffusion equation, partial derivative(t)u(epsilon) - del . (a(epsilon)delu(epsilon)) + g(u(epsilon)) = h(epsilon) in a bounded domain Omega with periodic microstructure F-(epsilon) boolean OR (M) over bar ((epsilon)), where a(epsilon)(x) is of order 1 in F-(epsilon) and kappa(epsilon) in M-(epsilon) with kappa(epsilon) --> 0 as epsilon --> 0. Combining the method of two-scale convergence and the variational homogenization we obtain effective models which depend on the parameter theta = lim(epsilon-->0) kappa(epsilon)/epsilon(2). In the case of strictly positive finite theta the effective problem is nonlocal in time that corresponds to the memory effect. (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.