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arXiv · 2007.01406

Radial regular and rupture solutions for a MEMS model with fringing field

Marius Ghergu·Yasuhito Miyamoto
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Abstract

We investigate radial solutions for the problem \[ \begin{cases} \displaystyle -\Delta U=\frac{\lambda+\delta|\nabla U|^2}{1-U},\; U>0 & \textrm{in}\ B,\\ U=0 & \textrm{on}\ \partial B, \end{cases} \] which is related to the study of Micro-Electromechanical Systems (MEMS). Here, $B\subset \mathbb{R}^N$ $(N\geq 2)$ denotes the open unit ball and $\lambda, \delta>0$ are real numbers. Two classes of solutions are considered in this work: (i) {\it regular solutions}, which satisfy $0 0$ is also discussed.

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Marius Ghergu, Yasuhito Miyamoto. 2020-07-02. Radial regular and rupture solutions for a MEMS model with fringing field. https://doi.org/10.1090/proc/15861

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