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

研究成果: Article

6 被引用数 (Scopus)

抄録

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).

本文言語English
ページ(範囲)301-323
ページ数23
ジャーナルNonlinear Analysis, Theory, Methods and Applications
66
2
DOI
出版ステータスPublished - 2007 1 15
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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