Dynamical solutions of singular parabolic equations modeling electrostatic MEMS

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We study the electrostatic MEMS-device parabolic equation, $${u_{t} - \Delta u = \frac{\lambda_{\rho}(x)}{(1 - u)^{2}}}$$ with Dirichlet boundary condition and a bounded domain $${\Omega}$$ of $${\mathbb{R}^{N}}$$ . Here $${\lambda}$$ is positive parameter and $${\rho}$$ is a nonnegative continuous function. In this paper, we investigate the behavior of solutions for this problem. In particular, we show small initial value yields quenching behavior of the solutions. While large initial data leads global existence of the solutions.