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.
Journal of Differential Equations, 264, 3285- 3311