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SeMA Journal

, Volume 61, Issue 1, pp 19–47 | Cite as

Polynomial decay rate for a wave equation with general acoustic boundary feedback laws

  • Z. Abbas
  • S. NicaiseEmail author
Article

Abstract

We consider the stabilization of the wave equation by a general class of acoustic boundary feedback laws at one extremity. This system is not uniformly stable but we furnish sufficient conditions that guarantee a polynomial stability. Our method combines the use of an observability inequality for the associated undamped problem obtained via sharp spectral results with regularity results of the solution of the undamped problem with a specific right-hand side. In some particular cases, the optimality of the decay is shown again with the help of precise spectral results of the operator associated with the damped problem. We illustrate our general results by some examples.

Keywords

Acoustic boundary control Stability Polynomial decay 

Mathematics Subject Classification (2000)

35L05 93D15 

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Copyright information

© Sociedad Española de Matemática Aplicada 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et ses Applications de Valenciennes, FR CNRS 2956, Institut des Sciences et Techniques de ValenciennesUniversité de Valenciennes et du Hainaut-CambrésisValenciennes Cedex 9France

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