Upscaling of a diffusion problem with flux jump in high contrast composites

Abstract

We study a diffusion problem in a periodic fibered composite consisting of two materials with highly contrasting diffusion coefficients. An important feature of our problem is the existence of an imperfect interface between the two phases of the composite medium, characterized by the continuity of the solution and the presence of a jump flux. By applying suitable homogenization techniques, we get the limit problems corresponding to two different choices for the flux jump.