Exponential decay for solutions to semilinear damped wave equation

Stéphane Gerbi; Belkacem Said-Houari

doi:10.3934/dcdss.2012.5.559

Exponential decay for solutions to semilinear damped wave equation

Stéphane Gerbi, Belkacem Said-Houari

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing 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].

Original language	English (US)
Pages (from-to)	559-566
Number of pages	8
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	5
Issue number	3
DOIs	https://doi.org/10.3934/dcdss.2012.5.559
State	Published - Oct 21 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The second author was supported by MIRA 2007 project of the Region Rhone-Alpes. This author wishes to thank Univ. de Savoie of Chambery for its kind hospitality. Moreover, the two authors wish to thank the referee for his useful remarks and his careful reading of the proofs presented in this paper.

ASJC Scopus subject areas

Analysis
Applied Mathematics
Discrete Mathematics and Combinatorics

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10.3934/dcdss.2012.5.559

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N2 - This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing 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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Exponential decay for solutions to semilinear damped wave equation

Abstract

Bibliographical note

ASJC Scopus subject areas

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