A nonlinear damped transmission problem as limit of wave equations with concentrating nonlinear terms away from the boundary

Abstract

In this paper we study an initial and boundary value problem for damped wave equations with nonlinear singular terms concentrating away from the boundary of the domain, on an interior neighbourhood of a hyper-surface M that collapses to M as ɛ goes to zero. We describe the conditions for well posedness of both the approximating and limit problems, as well as the convergence, at the singular limit, of the solutions of the former to solutions of the latter, when the parameter ɛ goes to zero.