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VOL. 47.1 | 2007 Diffusion phenomenon for abstract wave equations with decaying dissipation
Taeko Yamazaki

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Abstract

We consider the initial value problem of the abstract wave equation with dissipation whose coefficient tends to 0 as $t \to \infty$. 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. In the case that $H = L^2 (\mathbb{R}^n)$ and $A$ is the Laplace operator and $b(t)$ is a positive valued monotone $C^2$ function satisfying the sufficient assumption, Wirth obtained the decay estimate of the difference between the solution of the dissipative wave equation and the solution of the corresponding heat equation. The purpose of this paper is to show the decay estimate of the difference between the solution of the abstract wave equation with decaying dissipative term and the solution of the corresponding abstract parabolic equation.

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

MathSciNet: MR2387245

Digital Object Identifier: 10.2969/aspm/04710363

Rights: Copyright © 2007 Mathematical Society of Japan

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