[Une méthode directe pour la stabilisation de quelques équations des ondes semi-linéaires localement amorties]
Dans un premier temps, nous considérons une équation des ondes semi-linéaire avec un amortissement localement distribué dans un domaine borné. A l'aide de l'inégalité de Carleman, nous construisons une preuve élémentaire et directe de la décroissance exponentielle de l'énergie de ce système. Par la suite, nous appliquons la même technique pour étudier la stabilisation du même type d'équation dans l'espace tout entier. Nos démontrations sont constructives, et beaucoup plus simples que celles existantes.
First, we consider a semilinear wave equation with a locally distributed damping in a bounded domain. Using the Carleman estimate, we devise an elementary proof of the exponential decay of the energy of this system. Afterwards we apply the same technique to the stabilization of the same type of equation in the whole space. Our proofs are constructive, and much simpler than those found in the literature.
Publié le :
@article{CRMATH_2006__342_11_859_0,
author = {Tcheugou\'e T\'ebou, Louis},
title = {A direct method for the stabilization of some locally damped semilinear wave equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {859--864},
publisher = {Elsevier},
volume = {342},
number = {11},
year = {2006},
doi = {10.1016/j.crma.2006.04.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.04.010/}
}
TY - JOUR AU - Tcheugoué Tébou, Louis TI - A direct method for the stabilization of some locally damped semilinear wave equations JO - Comptes Rendus. Mathématique PY - 2006 SP - 859 EP - 864 VL - 342 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.04.010/ DO - 10.1016/j.crma.2006.04.010 LA - en ID - CRMATH_2006__342_11_859_0 ER -
%0 Journal Article %A Tcheugoué Tébou, Louis %T A direct method for the stabilization of some locally damped semilinear wave equations %J Comptes Rendus. Mathématique %D 2006 %P 859-864 %V 342 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.04.010/ %R 10.1016/j.crma.2006.04.010 %G en %F CRMATH_2006__342_11_859_0
Tcheugoué Tébou, Louis. A direct method for the stabilization of some locally damped semilinear wave equations. Comptes Rendus. Mathématique, Tome 342 (2006) no. 11, pp. 859-864. doi : 10.1016/j.crma.2006.04.010. http://www.numdam.org/articles/10.1016/j.crma.2006.04.010/
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