Well-posedness and general energy decay of solution for transmission problem with weakly nonlinear dissipative

Abstract

In this paper, we consider a transmission problem in a bounded domain with a nonlinear dissipation in the first equation. Under suitable assumptions on the weight of the damping, we show the existence and uniqueness of solution by the Faedo–Galerkin method. Also we prove general stability estimates using some properties of convex functions and Lyaponov functional.