Asymptotic analysis of a multiscale parabolic problem with a rough fast oscillating interface

Abstract

This paper is concerned with the well posedness and homogenization for a multiscale parabolic problem in a cylinder Q of $${\mathbb {R}}^N $$ . A rapidly oscillating non-smooth interface inside Q separates the cylinder in two heterogeneous connected components. The interface has a periodic microstructure, and it is situated in a small neighborhood of a hyperplane which separates the two components of Q. The problem models a time-dependent heat transfer in two heterogeneous conducting materials with an imperfect contact between them. At the interface, we suppose that the flux is continuous and that the jump of the solution is proportional to the flux. On the exterior boundary, homogeneous Dirichlet boundary conditions are prescribed. We also derive a corrector result showing the accuracy of our approximation in the energy norm.