Quenching Phenomenon for a Parabolic MEMS Equation

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 ? ^N , with Dirichlet boundary condition, an initial condition u₀(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, u₀(x). Finally, a global existence in the MEMS modeling is shown.