Advances in Differential Equations

Asymptotic behavior for abstract wave equations with decaying dissipation

Taeko Yamazaki

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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. 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.

Article information

Source
Adv. Differential Equations Volume 11, Number 4 (2006), 419-456.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867703

Mathematical Reviews number (MathSciNet)
MR2215622

Zentralblatt MATH identifier
1103.35081

Subjects
Primary: 35L90: Abstract hyperbolic equations
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35L15: Initial value problems for second-order hyperbolic equations

Citation

Yamazaki, Taeko. Asymptotic behavior for abstract wave equations with decaying dissipation. Adv. Differential Equations 11 (2006), no. 4, 419--456. https://projecteuclid.org/euclid.ade/1355867703.


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