Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 57, No. 3, pp. 285-310 (2000)

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Exponential Stability for The Wave Equation with Weak Nonmonotone Damping

Patrick Martinez and Judith Vancostenoble

M.I.P. Université Paul Sabatier Toulouse III,
118 route de Narbonne, 31062 Toulouse Cedex 4 - FRANCE
E-mail: martinez@mip.ups-tlse.fr
M.I.P. Université Paul Sabatier Toulouse III,
118 route de Narbonne, 31062 Toulouse Cedex 4 -- FRANCE
E-mail: vancoste@mip.ups-tlse.fr

Abstract: We consider the wave equation with a weak nonlinear internal damping. First for a weak monotone damping in dimension $2$, we prove that the energy of strong solutions decays exponentially to zero. This improves earlier results of Komornik and Nakao.
Then we consider a class of nonmonotone dampings. For strong solutions, we give new results of strong asymptotic stability and we prove that the energy decays to zero with an explicit decay rate estimate.

Keywords: Wave equation; weak damping; strong asymptotic stability; partition of the domain; rate of growth at infinity.

Classification (MSC2000): 26A12, 35B40, 93D15.

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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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