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

Mitsuhiro Nakao

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)25-42
Number of pages18
JournalIsrael Journal of Mathematics
Volume95
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

Decay of Solutions
Wave equation
Dissipation
Semilinear Wave Equation
Decay Estimates
Smooth Solution
Open set
Global Existence
Initial-boundary-value Problem
Non-negative
Decay
Boundary conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Decay of solutions of the wave equation with a local degenerate dissipation. / Nakao, Mitsuhiro.

In: Israel Journal of Mathematics, Vol. 95, 1996, p. 25-42.

Research output: Contribution to journalArticle

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