The Neumann boundary value problem for the Ginzburg-Landau heat flow equation:in a porous medium is considered. The so-called weakly connected domain #x3A9;(s)is taken as a model of the porous medium. Here s stands for a positive integer that characterizes the scale of the microstructure. It is shown that the homogenized model is a two-phase one. The coefficients of the homogenized equations are obtained by some local characteristics of the domain.
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