Exponential decay for solutions to semilinear damped wave equation

Stéphane Gerbi; Belkacem Said-Houari

doi:10.3934/dcdss.2012.5.559

Article Contents

2012, Volume 5, Issue 3: 559-566. Doi: 10.3934/dcdss.2012.5.559

This issue Previous Article Alternating proximal algorithm with costs-to-move, dual description and application to PDE's Next Article Some singular perturbations results for semilinear hyperbolic problems

Exponential decay for solutions to semilinear damped wave equation

Stéphane Gerbi^1, and
Belkacem Said-Houari^2,

1.
Laboratoire de Mathématiques, Université de Savoie, 73376 Le Bourget du Lac
2.
Division of Mathematical and Computer Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900

Received: February 28, 2010

Revised: April 30, 2010

Published: May 2012

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Abstract

This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].

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Mathematics Subject Classification: Primary: 35L70, 35B40.

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References

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