The point-wise estimates for the solution of damped wave equation with  nonlinear convection in multi-dimensional space

Jiao Chen; Weike Wang

doi:10.3934/cpaa.2014.13.307

Article Contents

2014, Volume 13, Issue 1: 307-330. Doi: 10.3934/cpaa.2014.13.307

This issue Previous Article Stable weak solutions of weighted nonlinear elliptic equations Next Article Vanishing viscosity limits for space-time periodic Hamilton-Jacobi equations

The point-wise estimates for the solution of damped wave equation with nonlinear convection in multi-dimensional space

Jiao Chen^1, and
Weike Wang^2,

1.
Mathematics department, Shanghai Jiao Tong University, Shanghai 200240
2.
Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai

Received: December 31, 2012

Revised: April 30, 2013

Published: December 2013

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Abstract

In this paper, we study the time-asymptotic behavior of the solution for the Cauchy problem of the damped wave equation with a nonlinear convection term in the multi-dimensional space. When the initial data is a small perturbation around a constant state $u^*$, we obtain the point-wise decay estimates of the solution under the so-called dissipative condition $|b| < 1$, where $b$ depends on $u^*$ and the nonlinear term.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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