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Dynamical solutions of singular parabolic equations modeling electrostatic MEMS

Article

Abstract

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.

Keywords

MEMS equation Quench Globally bounded 

Mathematics Subject Classification

35B44 35K10 35K20 35K58 35K91 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiChina

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