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

Yongqin Liu; Weike Wang

doi:10.3934/dcds.2008.20.1013

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2008, Volume 20, Issue 4: 1013-1028. Doi: 10.3934/dcds.2008.20.1013

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

Yongqin Liu^1, and
Weike Wang^2,

1.
School of Mathematical Sciences, Fudan University, Shanghai
2.
Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai

Received: February 2007

Revised: November 2007

Published: October 2008

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Abstract

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.

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Mathematics Subject Classification: 35E, 35L.

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