Decay of solutions of the wave equation with a local degenerate dissipation

Mitsuhiro Nakao

研究成果: Article査読

56 被引用数 (Scopus)

抄録

We derive a precise decay estimate of the solutions to the initial-boundary value problem for the wave equation with a dissipation: utt - Δu + a(cursive Greek chi)ut = 0 in Ω × [0, ∞) with the boundary condition u|∂Ω = 0, where a(cursive Greek chi) is a nonnegative function on Ω̄ satisfying a(cursive Greek chi) > 0 a.e. cursive Greek chi ∈ ω and ∫ω1/a(cursive Greek chi)pdcursive Greek chi < ∞ for some 0 < p < 1 for an open set ω ⊂ Ω̄ including a part of ∂Ω with a specific property. The result is applied to prove a global existence and decay of smooth solutions for a semilinear wave equation with such a weak dissipation.

本文言語English
ページ(範囲)25-42
ページ数18
ジャーナルIsrael Journal of Mathematics
95
出版ステータスPublished - 1996
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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