Pde problems with concentrating terms near the boundary

Abstract

En este artículo mostramos cómo convergen las soluciones de una ecuación de onda con amortiguamiento distribuido cerca del límite a las soluciones de una ecuación de onda con amortiguamiento de retroalimentación de límite. Se dan condiciones suficientes para que la convergencia de soluciones ocurra en el espacio de energía natural.

In this paper we study several PDE problems where certain linear or nonlinear termsin the equation concentrate in the domain, typically (but not exclusively) near the boundary. We analyze some linear and nonlinear elliptic models, linear and nonlinear parabolic ones as well as some damped wave equations. We show that in all these singularly perturbed problems, the concentrating terms give rise in the limit to a modification in the original boundary condition of the problem. Hence we describe in each case which is the singular limit problem and analyze the convergence of solutions.