Electron. J. Diff. Equ., Vol. 2013 (2013), No. 113, pp. 1-6.

Decay of solutions for a system of nonlinear wave equations

Xiao Wei

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.

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Xiao Wei
School of Science, Chang'An University
Xi'an 710064, China
email: xiaowei1802002@163.com

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