Equation with boundary feedback damping

Abstract

In this paper we consider PDE problems in which certain terms of the equations are concentrated,when a parameter tends to zero. Usually near the domain boundary.This implies that the problem in question is subject to singular perturbations that drastically changethe nature of the problem, by passing the limit on this parameter. The objective is then to identify theform of the limit problem and to describe the process of convergence of solutions, when this parametertends to zero. Here we consider a nonlinear PDE problem that is a generalization from previous workssuch as [1, 2].

In this paper we consider PDE problems in which certain terms of the equations are concentrated,when a parameter tends to zero. Usually near the domain boundary.This implies that the problem in question is subject to singular perturbations that drastically changethe nature of the problem, by passing the limit on this parameter. The objective is then to identify theform of the limit problem and to describe the process of convergence of solutions, when this parametertends to zero. Here we consider a nonlinear PDE problem that is a generalization from previous workssuch as [1, 2].