Energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations

Mitsuhiro Nakao*

*この研究の対応する著者

研究成果: Article査読

74 被引用数 (Scopus)

抄録

We derive the total energy decay E(t) ≤ I0(1 + t)-1 and L2 boundedness ∥u(t)∥2 ≤ CIo for the solutions to the initial boundary value problem for the wave equation in an exterior domain Ω: utt - Δu + a(x)ut = 0 in Ω × (0, ∞) with u(x, 0) = u0(x), ut(x, 0) = u1(x) and u|∂Ω = 0, where I0 = ∥u0∥H1 + ∥u12 and a(x) is a nonnegative function which is positive near some part of the boundary ∂Ω and near infinity. We apply these estimates to prove the global existence of decaying solutions for semilinear wave equations with nonlinearity f(u) like |u|αu, α > 0. We note that no geometrical condition is imposed on the boundary ∂Ω.

本文言語English
ページ(範囲)781-797
ページ数17
ジャーナルMathematische Zeitschrift
238
4
DOI
出版ステータスPublished - 2001 12月
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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