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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