  The singular parabolic problem $u_t=\Delta u -\frac{\lambda f(x)}{(1+u)^2}$
on a bounded domain $\Omega$ of $R^N$ with Dirichlet boundary conditions,
models the dynamic deflection of an elastic membrane in a simple electrostatic
Micro-Electromechanical System (MEMS) device. In this paper, we analyze and
estimate the quenching time of the elastic membrane in terms of the applied
voltage --represented here by $\lambda$. As a byproduct, we prove that for
sufficiently large $\lambda$, finite-time quenching must occur near the maximum
point of the varying dielectric permittivity profile $f(x)$.
