Asymptotic behavior for abstract wave equations with decaying dissipation

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

We consider the initial-value problem of the abstract wave equation with dissipation whose coefficient tends to 0 as t → ∞. In the case that the coefficient of the dissipation is a positive constant, Ikehata-Nishihara and Chill-Haraux obtained the decay estimate of the difference between the solution of this equation and the solution of the corresponding abstract heat equation. The purpose of this paper is to show the decay estimate of the difference between the solution of the above equation and the solution of the corresponding abstract parabolic equation. We also show the decay estimate for the solution of this dissipative wave equation.

Original languageEnglish
Pages (from-to)419-456
Number of pages38
JournalAdvances in Differential Equations
Volume11
Issue number4
Publication statusPublished - 1 Dec 2006

    Fingerprint

Cite this