Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898949 | Journal of Differential Equations | 2018 | 27 Pages |
Abstract
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. First, 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jong-Shenq Guo, Bei Hu,