Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Mitsuhiro Nakao

doi:10.2969/jmsj/06430851

Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Mitsuhiro Nakao^*

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u| ^αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.

Original language	English
Pages (from-to)	851-883
Number of pages	33
Journal	Journal of the Mathematical Society of Japan
Volume	64
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/06430851
Publication status	Published - 2012
Externally published	Yes

Keywords

Energy decay
Localized dissipation
Nonlinear wave equation

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06430851

Cite this

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abstract = "We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u| αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.",

keywords = "Energy decay, Localized dissipation, Nonlinear wave equation",

author = "Mitsuhiro Nakao",

year = "2012",

doi = "10.2969/jmsj/06430851",

language = "English",

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pages = "851--883",

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AU - Nakao, Mitsuhiro

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N2 - We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u| αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.

AB - We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation in exterior domains with a nonlinear localized dissipation. Our equation includes an absorbing term like |u| αu, α ≥ 0, and can be regarded as a generalized Klein-Gordon equation at least if α is closed to 0. This observation plays an essential role in our argument.

KW - Energy decay

KW - Localized dissipation

KW - Nonlinear wave equation

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JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

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ER -

Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

Abstract

Keywords

ASJC Scopus subject areas

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