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

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2009, 2009(Special): 592-601. doi: 10.3934/proc.2009.2009.592

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

1.	Hiratsuka, Kanagawa, 259-1292, Japan

Received August 2008 Revised August 2009 Published September 2009

Abstract
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In this paper we study the Cauchy problem for the weakly coupled system of damped wave equations. Recently Sun and Wang [12] have shown the existence and nonexistence of the Cauchy problem for the weakly coupled system of damped wave equations, provided that the space dimension $n=1, 3$. In this paper we will generalize their existence result to the case where $n=1,2.3$, and we improve time decay estimates when $n=3$. Moreover, the Cauchy problem with slow decaying initial data is treated.

Keywords: Cauchy problem, Damped wave equation, Weakly coupled system.

Mathematics Subject Classification: Primary: 35L55, 35L15, 35L70.

Citation: Takashi Narazaki. Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations. Conference Publications, 2009, 2009 (Special) : 592-601. doi: 10.3934/proc.2009.2009.592

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