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    题名: Quenching rate for a nonlocal problem arising in the micro-electro mechanical system
    作者: Guo, Jong-Shenq;Hu, Bei
    关键词: Quenching;Micro-electro mechanical system (MEMS);Lyapunov function;Non-local;Self-similar;Asymptotic
    日期: 2018-03
    上传时间: 2018-09-18 12:10:35 (UTC+8)
    摘要: In this paper, we study the quenching rate of the solution for a nonlocal parabolic problem which arises
    in the study of the micro-electro mechanical system. This question is equivalent to the stabilization of the
    solution to the transformed problem in self-similar variables. some a priori estimates are provided. In
    order to construct a Lyapunov function, due to the lack of time monotonicity property, we then derive some very useful and challenging estimates by a delicate analysis. Finally, with this Lyapunov function, we prove that the quenching rate is self-similar which is the same as the problem without the nonlocal term, except the constant limit depends on the solution itself.
    關聯: Journal of Differential Equations, 264, 3285- 3311
    DOI: 10.1016/j.jde.2017.11.017
    显示于类别:[數學學系暨研究所] 期刊論文

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