Geodesic
A corrector for a wave problem with periodic coefficients in a 1D bounded domain
Casado-Díaz, Juan1  ; Couce-Calvo, Julio1 ; Maestre, Faustino1 ; Martín-Gómez, José D.1
1 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 465-486

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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 H 1 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.

Reçu le :
DOI : 10.1051/cocv/2014034
Classification : 35B27, 35L20
Keywords: Wave equation, highly oscillating coefficients, homogenization, corrector, boundary conditions

Casado-Díaz, Juan 1 ; Couce-Calvo, Julio 1 ; Maestre, Faustino 1 ; Martín-Gómez, José D. 1

1 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain. 
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     author = {Casado-D{\'\i}az, Juan and Couce-Calvo, Julio and Maestre, Faustino and Mart{\'\i}n-G\'omez, Jos\'e D.},
     title = {A corrector for a wave problem with periodic coefficients in a {1D} bounded domain},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {465--486},
     publisher = {EDP-Sciences},
     volume = {21},
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     year = {2015},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014034/}
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Casado-Díaz, Juan; Couce-Calvo, Julio; Maestre, Faustino; Martín-Gómez, José D. A corrector for a wave problem with periodic coefficients in a 1D bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 465-486. doi: 10.1051/cocv/2014034

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