Global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation

Mitsuhiro Nakao

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Abstract

We discuss the existence of global or periodic solutions to the nonlinear wave equation [utt - Δu + ρ(x, ut) + β(x, u) = f (x, t) εΩ x R+(R ] with the boundary condition u ∂Ω, where Ω is a bounded domain in RN, ρ(x, ν) is a function like ρ(x, ν) = a(x)g(ν) with g′(ν) ≥0 and β(x, u) is a source term of power nonlinearity. a(x) is assumed to be positive only in a neighborhood of a part of the boundary ∂Ω and the stability property is very delicate, which makes the problem interesting.

Original languageEnglish
Pages (from-to)81-107
Number of pages27
JournalJournal of Differential Equations
Volume190
Issue number1
DOIs
Publication statusPublished - 2003 May 1
Externally publishedYes

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ASJC Scopus subject areas

  • Analysis

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