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

Mitsuhiro Nakao*

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)765-795
ページ数31
ジャーナルJournal of the Mathematical Society of Japan
55
3
出版ステータスPublished - 2003 7月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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