PORTUGALIAE MATHEMATICA Vol. 55, No. 3, pp. 293306 (1998) 

On the Decay Estimates for the Wave Equation with a Local Degenerate or Nondegenerate DissipationLouis Roder Tcheugoué TébouI.R.M.A., Université Louis Pasteur et C.N.R.S,7, rue René Descartes, 67084 Strasbourg Cedex  FRANCE Email: kouemou@math.ustrasbg.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 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
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