On semilinear elliptic equation with negative exponent arising from a closed MEMS model
On semilinear elliptic equation with negative exponent arising from a closed MEMS model
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DOI：
10.1007/s00033-023-02116-4
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Huyuan Chen;Y. Wang;F. Zhou
中科院分区：
文献类型：
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作者：
Huyuan Chen;Y. Wang;F. Zhou
本文研究了连通有界区域上的椭圆型方程在零Dirichlet边界条件下的解，其中，和在边界处为零，其速率为。当和时，该方程模拟了封闭的微机电系统器件，其中弹性膜在边界上粘附弯曲接地板，但在边界上绝缘。该功能塑造了弯曲的接地板。本文的目的是研究该方程的极小解的一些定性性质，并说明边界衰减对极小解的性质和吸合电压的影响。特别地，我们对极小解的稳定性进行了完整的分析。
This paper is concerned with the elliptic equationin a connected, boundeddomainofsubject to zero Dirichlet boundary conditions, where,andvanishes at the boundary with the ratefor. Whenand, this equation models the closed micro-electromechanical systems devices, where the elastic membrane sticks the curved ground plate on the boundary, but insulating on the boundary. The functionashapes the curved ground plate. Our aim in this paper is to study some qualitative properties of minimal solutions of this equation when,and to show how the boundary decaying ofaworks on the behavior of minimal solutions and the pull-in voltage. Particularly, we give a complete analysis for the stability of the minimal solutions.