Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 55, No. 3, pp. 293-306 (1998)

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On the Decay Estimates for the Wave Equation with a Local Degenerate or Nondegenerate Dissipation

Louis Roder Tcheugoué Tébou

I.R.M.A., Université Louis Pasteur et C.N.R.S,
7, rue René Descartes, 67084 Strasbourg Cedex - FRANCE
E-mail: kouemou@math.u-strasbg.fr

Abstract: In a bounded domain, we consider the wave equation with a local dissipation. We prove the polynomial decay of the energy for a degenerate dissipation and the exponential decay of the energy for a nondegenerate dissipation. The method of proof is direct and is based on multipliers technique, on some integral inequalities due to Haraux and on a judicious idea of Conrad and Rao.

Keywords: Wave equation; decay estimates; local dissipation; degenerate dissipation; integral inequalities.

Classification (MSC2000): 35L05, 93D15

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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