FIRST ORDER ASYMPTOTIC EXPANSION FOR A SINGULARLY PERTURBED, COUPLED PARABOLIC-PARABOLIC PROBLEM

Abstract

In this paper we consider the coupled problem (S_e), (BC_e), (IC_e), (TC_e) formulated below, where e is a positive small parameter. This is a singularly perturbed problem with an internal transition layer along the coupling boundary. A first order asymptotic expansion of the solution is established, including some transition layer corrections. Estimates for the remainder terms with respect to the uniform convergence norm are proved in order to validate the expansion.