Homogenization for thermoconductivity in a porous medium with periods of different orders in the different directions

Article type: Research Article

Authors: Bakhvalov, N.S.^; | Saint Jean Paulin, J.

Affiliations: Moscow State University, Department of Mechanics and Mathematics, Lenin's hills, 119899 Moscow, Russia | Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France

Note: [] The work of N.S. Bakhvalov was partially supported by the Russian Foundation for basic research, 93-01-01729, and most of it was done while he enjoyed the hospitality of the Mathematics Department of the University of Metz.

Abstract: We study here the problem of heat transfer in a porous medium consisting of a homogeneous isotropic material. We assume that the period of the medium is not the same in the two directions and that the ratio of these two periods tends to zero. We find the explicit representation of the coefficients of the averaged equations and prove strong convergence to the solution of the averaged problem.

DOI: 10.3233/ASY-1996-13302

Journal: Asymptotic Analysis, vol. 13, no. 3, pp. 253-276, 1996