Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition

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December 2005, 4(4): 861-869. doi: 10.3934/cpaa.2005.4.861

Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition

1.	Department of Mathematics, Henan University of Technology, Zhengzhou 450052, China, China

Received October 2004 Revised May 2005 Published September 2005

Abstract
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In this paper the asymptotic behavior and nonexistence of solution for the wave equation $u_{t t}-\Delta u=0$ with nonlinear boundary condition $\frac {\partial u}{\partial \nu}=-|u_t|^{m-2}u_t+|u|^{p-2}u$ are given.

Keywords: nonexistence of solution, nonlinear boundary condition, asymptotic behavior of solution, Wave equation.

Mathematics Subject Classification: Primary: 35L70, 35L20.

Citation: Hongwei Zhang, Qingying Hu. Asymptotic behavior and nonexistence of wave equation with nonlinear boundary condition. Communications on Pure & Applied Analysis, 2005, 4 (4) : 861-869. doi: 10.3934/cpaa.2005.4.861

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