Advances in Differential Equations

Scattering and modified scattering for abstract wave equations with time-dependent dissipation

Jens Wirth

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Abstract

We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related to solutions of the free problem multiplied by a decay function. This paper gives the counterpart to a recent paper of T. Yamazaki [Adv. Differential Equ., 11(4):419--456, 2006], where effective dissipation terms and the relation to the corresponding abstract parabolic problem are considered.

Article information

Source
Adv. Differential Equations, Volume 12, Number 10 (2007), 1115-1133.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1367241160

Mathematical Reviews number (MathSciNet)
MR2362265

Zentralblatt MATH identifier
1159.35047

Subjects
Primary: 35L90: Abstract hyperbolic equations
Secondary: 35P25: Scattering theory [See also 47A40]

Citation

Wirth, Jens. Scattering and modified scattering for abstract wave equations with time-dependent dissipation. Adv. Differential Equations 12 (2007), no. 10, 1115--1133. https://projecteuclid.org/euclid.ade/1367241160


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