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arXiv · 2401.04128

Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS

Heiko Gimperlein·Runan He·Andrew A. Lacey
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Abstract

Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modelled by a semi-linear hyperbolic equation. The gap between the plates contains a gas and the gas pressure is taken to obey a quasi-linear parabolic Reynolds' equation. Local-in-time existence of strict solutions of the system is shown, using well-known local-in-time existence results for the hyperbolic equation, then H\"{o}lder continuous dependence of its solution on that of the parabolic equation, and finally getting local-in-time existence for a combined abstract parabolic problem. Semigroup approaches are vital for the local-in-time existence results.

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Heiko Gimperlein, Runan He, Andrew A. Lacey. 2024-01-05. Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS. https://doi.org/10.1002/mma.9922

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