Differential and Integral Equations

Global solutions to the Cauchy problem for a system of damped wave equations

Takashi Narazaki

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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.

Article information

Source
Differential Integral Equations, Volume 24, Number 5/6 (2011), 569-600.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356018919

Mathematical Reviews number (MathSciNet)
MR2809622

Zentralblatt MATH identifier
1249.35223

Subjects
Primary: 35L71: Semilinear second-order hyperbolic equations 35L52: Initial value problems for second-order hyperbolic systems 35L05: Wave equation

Citation

Narazaki, Takashi. Global solutions to the Cauchy problem for a system of damped wave equations. Differential Integral Equations 24 (2011), no. 5/6, 569--600. https://projecteuclid.org/euclid.die/1356018919


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