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

Mitsuhiro Nakao

Research output: Contribution to journalArticle

7 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 languageEnglish
Pages (from-to)851-883
Number of pages33
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number3
DOIs
Publication statusPublished - 2012
Externally publishedYes

Fingerprint

Energy Decay
Semilinear Wave Equation
Decay Estimates
Klein-Gordon Equation
Exterior Domain
Energy Estimates
Generalized Equation
Absorbing
Initial-boundary-value Problem
Dissipation
Closed
Term
Observation

Keywords

  • Energy decay
  • Localized dissipation
  • Nonlinear wave equation

ASJC Scopus subject areas

  • Mathematics(all)

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.",
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