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

Pages: 592 - 601, Issue Special, September 2009

 Abstract        Full Text (167.1K)              

Takashi Narazaki - Hiratsuka, Kanagawa, 259-1292, Japan (email)

Abstract: 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:  Damped wave equation, Weakly coupled system, Cauchy problem
Mathematics Subject Classification:  Primary: 35L55, 35L15, 35L70

Received: August 2008;      Revised: August 2009;      Published: September 2009.