American Institute of Mathematical Sciences

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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

Takashi Narazaki 1,

1. 

Hiratsuka, Kanagawa, 259-1292, Japan

Received  August 2008 Revised  August 2009 Published  September 2009

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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