Electron. J. Diff. Equ., Vol. 2013 (2013), No. 256, pp. 1-16.

Pointwise estimates for solutions to a system of nonlinear damped wave equations

Wenjun Wang

In this article, we consider the existence of global solutions and pointwise estimates for the Cauchy problem of a nonlinear damped wave equation. We obtain the existence by using the approach introduced by Li and Chen in [7] and some estimates of the solution. The proofs of the estimates are based on a detailed analysis of the Green function of the linear damped wave equations. Also, we show the L^p convergence rate of the solution.

Submitted June 24, 2013. Published November 20, 2013.
Math Subject Classifications: 35L15.
Key Words: Damped wave system; global solution; classical solution; pointwise estimate; Green function.

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Wenjun Wang
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: wwj001373@hotmail.com

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