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

 

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Opened Access A corrector for a wave problem with periodic coefficients in a 1D bounded domain
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Author: Casado Díaz, Juan
Couce Calvo, Julio
Maestre Caballero, Faustino
Martín Gómez, José Domingo
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015
Published in: ESAIM: Control, Optimisation and Calculus of Variations, 21 (2), 465-486.
Document type: Article
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 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.
Cite: Casado Díaz, J., Couce Calvo, J., Maestre Caballero, F. y Martín Gómez, J.D. (2015). A corrector for a wave problem with periodic coefficients in a 1D bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, 21 (2), 465-486.
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URI: http://hdl.handle.net/11441/42110

DOI: http://dx.doi.org/10.1051/cocv/2014034

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