Homogenization of the ginzburg—landau heat flow equation in a porous medium

Abstract

The Neumann boundary value problem for the Ginzburg-Landau heat flow equation:

in a porous medium is considered. The so-called weakly connected domain Ω^(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.

Keywords:

• Ginzburg-Landau heat flow equation
• weakly connected domains
• homogenization

AMS:

• 35B40
• 35Q55

¹ Mathematical Division, Institute for Low Temperature Physics, 47. Lenin ave., 310164, Kharkov, Ukraine, [email protected].

¹ Mathematical Division, Institute for Low Temperature Physics, 47. Lenin ave., 310164, Kharkov, Ukraine, [email protected].

Notes

¹ Mathematical Division, Institute for Low Temperature Physics, 47. Lenin ave., 310164, Kharkov, Ukraine, [email protected].