We consider a wave problem posed in a bounded open interval of , 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 topology, which for the wave equation is known to be non-local. In a previous paper we have studied this problem in the whole , 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.
DOI : 10.1051/cocv/2014034
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
@article{COCV_2015__21_2_465_0,
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},
year = {2015},
publisher = {EDP Sciences},
volume = {21},
number = {2},
doi = {10.1051/cocv/2014034},
zbl = {1320.35041},
mrnumber = {3348408},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2014034/}
}
TY - JOUR AU - Casado-Díaz, Juan AU - Couce-Calvo, Julio AU - Maestre, Faustino AU - Martín-Gómez, José D. TI - A corrector for a wave problem with periodic coefficients in a 1D bounded domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 465 EP - 486 VL - 21 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2014034/ DO - 10.1051/cocv/2014034 LA - en ID - COCV_2015__21_2_465_0 ER -
%0 Journal Article %A Casado-Díaz, Juan %A Couce-Calvo, Julio %A Maestre, Faustino %A Martín-Gómez, José D. %T A corrector for a wave problem with periodic coefficients in a 1D bounded domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 465-486 %V 21 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2014034/ %R 10.1051/cocv/2014034 %G en %F COCV_2015__21_2_465_0
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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