Energy decay and periodic solution for the wave equation in an exterior domain with half-linear and nonlinear boundary dissipations

Mitsuhiro Nakao, Jeong Ja Bae

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We first consider the wave equation in an exterior domain Ω in RN with two separated boundary parts Γ0, Γ1. On Γ0, the Dirichlet condition u |Γ0 = 0 is imposed, while on Γ1, Neumann type nonlinear boundary dissipation ∂ u / ∂ ν = - g (ut) is assumed. Further, a 'half-linear' localized dissipation is attached on Ω. For such a situation we derive a precise rate of decay of the energy E (t) for solutions of the initial boundary value problem. We impose no geometrical condition on the shape of the boundary ∂ Ω = Γ0 ∪ Γ1. Secondly, when a T periodic forcing term works we prove the existence of a T periodic solution on R under an additional growth assumption on ρ (x, v) and g (v).

Original languageEnglish
Pages (from-to)301-323
Number of pages23
JournalNonlinear Analysis, Theory, Methods and Applications
Volume66
Issue number2
DOIs
Publication statusPublished - 2007 Jan 15
Externally publishedYes

    Fingerprint

Keywords

  • Energy decay
  • Exterior domain
  • Nonlinear dissipation
  • Periodic solution
  • Wave equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this