1. Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS.
- Author
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Gimperlein, Heiko, He, Runan, and Lacey, Andrew A.
- Subjects
- *
REYNOLDS equations , *HOLDER spaces , *MICROELECTROMECHANICAL systems , *PARABOLIC operators , *HYPERBOLIC differential equations - Abstract
Local wellposedness for a nonlinear parabolic-hyperbolic coupled system modeling 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 modeled by a semilinear hyperbolic equation. The gap between the plates contains a gas and the gas pressure is taken to obey a quasilinear 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 Hölder 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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