Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 2, pp. 147-159 (2004)

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Stabilization of a wave-wave system

N. Aissa and D. Hamroun

USTHB, Faculté de Mathématiques,
BP 32 El Alia, Bab Ezzouar -- ALGER
E-mail: djamroun@yahoo.fr

Abstract: In this paper, we use the multiplier method to study the energy decay of a coupling of a wave equation posed on a square $\Omega $ of $\mathbb{R}^2$ with a wave equation posed on one of its sides $\Gamma_0$. We prove that if the dissipation is located both on $\Omega$ and $\Gamma_0$, then the energy decays exponentially.

Keywords: wave equation; semigroup; stability; multipliers.

Classification (MSC2000): 35B40, 35C20, 35L20, 35P20, 49N35.

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Electronic version published on: 7 Mar 2008.

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