October  2008, 20(4): 1013-1028. doi: 10.3934/dcds.2008.20.1013

The pointwise estimates of solutions for dissipative wave equation in multi-dimensions

1. 

School of Mathematical Sciences, Fudan University, Shanghai, China

2. 

Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai

Received  February 2007 Revised  November 2007 Published  January 2008

In this paper we focus on the pointwise estimates of the solution to the Cauchy problem for the dissipative wave equation in multi-dimensions. By using the method of Green function combined with the Fourier analysis, we obtain the pointwise estimates of the solution, which yields the $L^p(1\leq p\leq\infty)$ decay estimates of the solution.
Citation: Yongqin Liu, Weike Wang. The pointwise estimates of solutions for dissipative wave equation in multi-dimensions. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 1013-1028. doi: 10.3934/dcds.2008.20.1013
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