### 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| ^{α}u, 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 |
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Pages (from-to) | 851-883 |

Number of pages | 33 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 64 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- Energy decay
- Localized dissipation
- Nonlinear wave equation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term.** / Nakao, Mitsuhiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term

AU - Nakao, Mitsuhiro

PY - 2012

Y1 - 2012

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

UR - http://www.scopus.com/inward/record.url?scp=84866916068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866916068&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06430851

DO - 10.2969/jmsj/06430851

M3 - Article

AN - SCOPUS:84866916068

VL - 64

SP - 851

EP - 883

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 3

ER -