Diffusion through thin layers with high specific heat

Abstract

We study the asymptotic behaviour of the diffusion-transmission problem in a fixed domain surrounded by a layer whose thickness of order δ goes to zero and where the specific heat σ goes to infinity. We characterize essentially three limit cases according to the limit α of the product δσ: if α=0 or α=∞, we have a Neumann or a Dirichlet boundary condition respectively, while if 0<α<∞, we obtain a mixed boundary condition involving the trace of the time derivative. We also extend this result to a class of unilateral problems of Signorini type.