On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains

Mitsuhiro Nakao

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the initial-boundary value problem for the standard quasilinear wave equation: utt - div{σ(|∇u| 2)∇u} + a(x)ut = 0 in Ω × [0, ∞) u(x, 0) = u0(x) and ut(x, 0) = u1(x) and u|∂Ω = 0 where Ω is an exterior domain in R N, σ(v) is a function like σ(v) = 1/√1 + v and a(x) is a nonnegative function. Under two types of hypotheses on a(x) we prove existence theorems of global small amplitude solutions. We note that a(x)u t is required to be effective only in localized area and no geometrical condition is imposed on the boundary ∂Ω.

Original languageEnglish
Pages (from-to)765-795
Number of pages31
JournalJournal of the Mathematical Society of Japan
Volume55
Issue number3
Publication statusPublished - 2003 Jul
Externally publishedYes

Fingerprint

Quasilinear Wave Equation
Global Smooth Solution
Exterior Domain
Initial-boundary-value Problem
Existence Theorem
Non-negative
Standards

Keywords

  • Decay
  • Exterior domain
  • Global solution
  • Localized dissipation
  • Quasilinear wave equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On global smooth solutions to the initial-boundary value problem for quasilinear wave equations in exterior domains. / Nakao, Mitsuhiro.

In: Journal of the Mathematical Society of Japan, Vol. 55, No. 3, 07.2003, p. 765-795.

Research output: Contribution to journalArticle

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