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2007 Scattering and modified scattering for abstract wave equations with time-dependent dissipation
Jens Wirth
Adv. Differential Equations 12(10): 1115-1133 (2007).

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.

Citation

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Jens Wirth. "Scattering and modified scattering for abstract wave equations with time-dependent dissipation." Adv. Differential Equations 12 (10) 1115 - 1133, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1159.35047
MathSciNet: MR2362265

Subjects:
Primary: 35L90
Secondary: 35P25

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 10 • 2007
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