Energy decay for the wave equation with boundary and localized dissipations in exterior domains

Jeong Ja Bae, Mitsuhiro Nakao

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11 Citations (Scopus)

Abstract

We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain Ω with the boundary ∂Ω, = Γ0 ∪ Γ1, Γ0 ∩ Γ1 = Ø. We impose the homogeneous Dirichlet condition on Γ0 and a dissipative Neumann condition on Γ1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary Γ0. Under these assumptions we derive an energy decay like E(t) ≤ C(1 + t)-1 and some related estimates.

Original languageEnglish
Pages (from-to)771-783
Number of pages13
JournalMathematische Nachrichten
Volume278
Issue number7-8
DOIs
Publication statusPublished - 2005
Externally publishedYes

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Keywords

  • Dissipation
  • Energy decay
  • Exterior problem
  • Wave equation

ASJC Scopus subject areas

  • Mathematics(all)

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