Electron. J. Differential Equations, Vol. 2017 (2017), No. 161, pp. 1-12.

Observability inequality and decay rate for wave equations with nonlinear boundary conditions

Yuan Gao, Jin Liang, Ti-Jun Xiao

Abstract:
We study a class of wave propagation problems concerning the nonlinearity of dynamic evolution for boundary material. We establish an observability inequality for the related linear system, and make a connection between the linear system and the original nonlinear coupled system. Also, we obtain the desired energy decay rate for the original nonlinear boundary value problem.

Submitted September 8, 2016. Published July 4, 2017.
Math Subject Classifications: 35L70, 35B35, 76Q05, 35L20.
Key Words: Nonlinear wave; coupled boundary equations; uniform decay rates; observability inequality.

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Yuan Gao
Shanghai Key Laboratory for Contemporary Applied Mathematics
School of Mathematical Sciences
Fudan University
Shanghai 200433, China
email: gaoyuan12@fudan.edu.cn
Jin Liang
School of Mathematical Sciences
Shanghai Jiao Tong University
Shanghai 200240, China
email: jinliang@sjtu.edu.cn
Ti-Jun Xiao
Shanghai Key Laboratory for Contemporary Applied Mathematics
School of Mathematical Sciences
Fudan University
Shanghai 200433, China
email: tjxiao@fudan.edu.cn

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