A corrector for a wave problem with periodic coefficients in a 1D bounded domain

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain. ; ;
jcasadod@us.es; couce@us.es

Received: 5 March 2014
Revised: 12 June 2014

Abstract

We consider a wave problem posed in a bounded open interval of R, where the coefficients, the initial conditions and the right-hand side are highly oscillating, periodic in the space variable and almost periodic in the time one. Our purpose is to find not only the corresponding limit equation but a corrector, i.e. a strong approximation in the H¹ topology, which for the wave equation is known to be non-local. In a previous paper we have studied this problem in the whole R^N, here we consider the case of a bounded domain in dimension one. Thus the novelty in this paper is the analysis of the boundary conditions.