Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 1, pp. 81-96 (2004)

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Optimal energy decay rate of coupled wave equations

Ahmed Benaddi

Centro de Modelamiento Matemático, UMR 2071 CNRS-Uchile,
Casilla 170/3-Correo 3, Santiago -- CHILE
E-mail: benaddi@dim.uchile.cl

Abstract: We consider a system of coupled wave equations subject to positive viscous damping. Under the assumption that the damping function is of bounded variations, we give the asymptotic expansion of eigenvalues and eigenfunctions of the infinitesimal generator of the associated semigroup. Moreover, we prove that the eigenfunctions form a Riesz basis in the energy space.

Keywords: viscous damping; asymptotic expansion of the eigenvalues; Riesz basis; optimal decay rate.

Classification (MSC2000): 35C20, 35P20, 35P10, 93D15.

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Electronic version published on: 7 Mar 2008.

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