Energy decay to the Cauchy problem for a generalised nonlinear Klein-Gordon equation with a nonlinear dissipative term

Mitsuhiro Nakao

doi:10.1504/IJDSDE.2011.041880

Energy decay to the Cauchy problem for a generalised nonlinear Klein-Gordon equation with a nonlinear dissipative term

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We derive a precise decay rate of energy of solutions to the Cauchy problem for the wave equation with a nonlinear dissipative term and an absorbing term. Due to the absorbing term the equation is regarded as a generalised Klein-Gordon equation with a nonlinear dissipative term. This observation plays an important role in the proof.

Original language	English
Pages (from-to)	349-362
Number of pages	14
Journal	International Journal of Dynamical Systems and Differential Equations
Volume	3
Issue number	3
DOIs	https://doi.org/10.1504/IJDSDE.2011.041880
Publication status	Published - 2011 Aug
Externally published	Yes

Keywords

Energy decay
Nonlinear dissipation
Wave equation

ASJC Scopus subject areas

Engineering(all)
Discrete Mathematics and Combinatorics
Control and Optimization

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10.1504/IJDSDE.2011.041880

Cite this

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abstract = "We derive a precise decay rate of energy of solutions to the Cauchy problem for the wave equation with a nonlinear dissipative term and an absorbing term. Due to the absorbing term the equation is regarded as a generalised Klein-Gordon equation with a nonlinear dissipative term. This observation plays an important role in the proof.",

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author = "Mitsuhiro Nakao",

year = "2011",

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AB - We derive a precise decay rate of energy of solutions to the Cauchy problem for the wave equation with a nonlinear dissipative term and an absorbing term. Due to the absorbing term the equation is regarded as a generalised Klein-Gordon equation with a nonlinear dissipative term. This observation plays an important role in the proof.

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Energy decay to the Cauchy problem for a generalised nonlinear Klein-Gordon equation with a nonlinear dissipative term

Abstract

Keywords

ASJC Scopus subject areas

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