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Comptes Rendus Mathématique
Volume 342, n° 11
pages 859-864 (juin 2006)
Doi : 10.1016/j.crma.2006.04.010
accepted : 30 Mars 2006
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
 

Louis Tcheugoué Tébou
Department of Mathematics, Florida International University, Miami, FL 33199, USA 

Abstract

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. To cite this article: L. Tcheugoué Tébou, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.
Résumé

Dans un premier temps, nous considérons une équation des ondes semi-linéaire avec un amortissement localement distribué dans un domaine borné. A lʼaide de lʼinégalité de Carleman, nous construisons une preuve élémentaire et directe de la décroissance exponentielle de lʼénergie de ce système. Par la suite, nous appliquons la même technique pour étudier la stabilisation du même type dʼéquation dans lʼespace tout entier. Nos démontrations sont constructives, et beaucoup plus simples que celles existantes. Pour citer cet article : L. Tcheugoué Tébou, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.


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