Estimates for the quenching time of a MEMS equation with fringing field

作者：Wang, Qi^*

来源：Journal of Mathematical Analysis and Applications, 2013, 405(1): 135-147.

DOI：10.1016/j.jmaa.2013.03.054

• MEMS equation
• Fringing field
• Quenching time

In this paper we consider a zero initial-boundary value parabolic problem in MEMS with fringing field, u(t) - Delta(u) = lambda g(u)(1 delta vertical bar del u vertical bar(2)), in a bounded domain Omega of R-N. Here lambda > 0 is a parameter related to the applied voltage, delta > 0, g is a positive nondecreasing convex function, diverging as u -> 1. Firstly, we show that the solvability of the stationary problem - Delta w = lambda g (w)(1 delta vertical bar del w vertical bar(2)) with Dirichlet boundary condition is characterized by a parameter lambda*(delta). Meanwhile it is shown that for lambda > lambda*(delta), any solution to the parabolic equation will quench (u -> 1) at a finite time. Secondly, we focus on estimating the quenching time T*(delta) in terms of lambda, lambda*(delta), i.e. the quenching time T*(delta) = 0((lambda - lambda*(delta))-(1)/(2)), as lambda -> (lambda*(delta))( ).

• 出版日期2013-9-1
• 单位华东师范大学