Quenching phenomenon for a parabolic MEMS equation

Abstract

This paper deals with the electrostatic MEMS-device parabolic equation ${u_t} - \Delta u = \frac{{\lambda f(x)}}{{{{(1 - u)}^p}}}$ in a bounded domain Ω of ℝ ^N, with Dirichlet boundary condition, an initial condition u ₀(x) ∈ [0, 1) and a nonnegative profile f, where λ > 0, p > 1. The study is motivated by a simplified micro-electromechanical system (MEMS for short) device model. In this paper, the author first gives an asymptotic behavior of the quenching time T ^* for the solution u to the parabolic problem with zero initial data. Secondly, the author investigates when the solution u will quench, with general λ, u ₀(x). Finally, a global existence in the MEMS modeling is shown.

Keywords

MEMS equation / Quenching time / Global existence

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