The point-wise estimates of solutions for semi-linear dissipativewave equation

Yongqin Liu

doi:10.3934/cpaa.2013.12.237

Article Contents

2013, Volume 12, Issue 1: 237-252. Doi: 10.3934/cpaa.2013.12.237

This issue Previous Article On the homogenization of some non-coercive Hamilton--Jacobi--Isaacs equations Next Article Behaviour of $p$--Laplacian problems with Neumann boundary conditions when $p$ goes to 1

The point-wise estimates of solutions for semi-linear dissipative wave equation

Yongqin Liu^1,

1.
Department of Mathematics, North China Electric Power University, Beijing 102208

Received: April 30, 2011

Revised: August 31, 2011

Published: December 2012

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Abstract

In this paper we focus on the global-in-time existence and the point-wise estimates of solutions to the initial value problem for the semi-linear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the point-wise decay estimates of solutions to the problem.

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Mathematics Subject Classification: 35E15, 35L05, 35L15.

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