Quenching rate for a nonlocal problem arising in the micro-electro mechanical system

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/114915

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/114915

Title:	Quenching rate for a nonlocal problem arising in the micro-electro mechanical system
Authors:	Guo, Jong-Shenq;Hu, Bei
Keywords:	Quenching;Micro-electro mechanical system (MEMS);Lyapunov function;Non-local;Self-similar;Asymptotic
Date:	2018-03
Issue Date:	2018-09-18 12:10:35 (UTC+8)
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. 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.
Relation:	Journal of Differential Equations, 264, 3285- 3311
DOI:	10.1016/j.jde.2017.11.017
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	200	View/Open
Quenching rate for a nonlocal problem arising in the micro-electro mechanical system.pdf		346Kb	Adobe PDF	6	View/Open