A direct method for the stabilization of some locally damped semilinear wave equations

Louis Tcheugoué Tébou

doi:10.1016/j.crma.2006.04.010

Partial Differential Equations

A direct method for the stabilization of some locally damped semilinear wave equations
[Une méthode directe pour la stabilisation de quelques équations des ondes semi-linéaires localement amorties]

Présenté par : Haïm Brezis

Louis Tcheugoué Tébou ¹

¹ Department of Mathematics, Florida International University, Miami, FL 33199, USA

Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 859-864.

Résumé
Abstract

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.

Accepté le : 2006-03-30
Publié le : 2006-05-05

DOI : 10.1016/j.crma.2006.04.010

Affiliations des auteurs :

Louis Tcheugoué Tébou ¹

¹ Department of Mathematics, Florida International University, Miami, FL 33199, USA

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     title = {A direct method for the stabilization of some locally damped semilinear wave equations},
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Louis Tcheugoué Tébou. A direct method for the stabilization of some locally damped semilinear wave equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 859-864. doi : 10.1016/j.crma.2006.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.010/

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