Volume 21, Number 2, April-June 2015
|Page(s)||465 - 486|
|Published online||04 March 2015|
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.
Revised: 12 June 2014
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 RN, 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.
Mathematics Subject Classification: 35B27 / 35L20
Key words: Wave equation / highly oscillating coefficients / homogenization / corrector / boundary conditions
© EDP Sciences, SMAI, 2015
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