Some corrector results for composites with imperfect interface

Abstract

In this paper we give some corrector results for a problem modelling the stationary heat diffusion in a conductor with two components, a connected one Ω^ε_1 and a disconnected one Ω^ε_2, consisting of ε-periodic connected components of size ε. The flow of heat is proportional, by mean of a function of order εγ, γ > −1, to the jump of the temperature field, due to a contact resistance on the interface. We prove a corrector result for the temperature in the component Ω^ε_1. Moreover, for −1 1 needs to be treated separately. These results complete the study of the asymptotic behaviour of this problem done in [10].

Keywords

• homogenization
• correctors
• perforated domains
• jump boundary conditions