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May/June 2011 Global solutions to the Cauchy problem for a system of damped wave equations
Takashi Narazaki
Differential Integral Equations 24(5/6): 569-600 (May/June 2011).

Abstract

The Cauchy problem to the system of nonlinear damped wave equations is treated. Several authors have shown existence and asymptotic behavior of global solutions to the above problem when the space dimension is not greater than three. We will show the existence and asymptotic behavior of global solutions to the problem with rapidly decaying initial data when the space dimension is greater than three, where we apply estimates in weighted Sobolev spaces of the above solution operator. Moreover, using the theory of modulation spaces introduced by Feitinger [4], we will also show the existence and asymptotic behavior of global solutions to the problem with slowly decaying initial data.

Citation

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Takashi Narazaki. "Global solutions to the Cauchy problem for a system of damped wave equations." Differential Integral Equations 24 (5/6) 569 - 600, May/June 2011.

Information

Published: May/June 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35223
MathSciNet: MR2809622

Subjects:
Primary: 35L05, 35L52, 35L71

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 5/6 • May/June 2011
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