Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 113, pp. 1-6.
Title: Decay of solutions for a system of nonlinear wave equations
Author: Xiao Wei (Chang'An University, Xi'an 710064, China)
Abstract:
This article concerns the decay of solutions
of the semi-linear wave equation
$$
u_{tt}+\delta u_t-\phi(x)\triangle u=\lambda u|u|^{\beta-1}\quad
x\in \mathbb{R}^N\; t\geq0
$$
Introducing an appropriate Lyaponuv function, we find
exponential decay for certain initial data.
Submitted December 28, 2012. Published April 30, 2013.
Math Subject Classifications: 35B40, 35L10.
Key Words: Nonlinear wave equations; initial boundary value problem;
exponential decay.