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Quenching phenomenon for a parabolic MEMS equation

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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 ℝN, 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.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Qi Wang

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  1. Qi Wang
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Correspondence to Qi Wang.

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Wang, Q. Quenching phenomenon for a parabolic MEMS equation. Chin. Ann. Math. Ser. B 39, 129–144 (2018). https://doi.org/10.1007/s11401-018-1056-6

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  • DOI: https://doi.org/10.1007/s11401-018-1056-6

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