Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS
arXiv:2401.04128 · doi:10.1002/mma.9922
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 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.
40 pages, 1 figure, to appear in Mathematical Methods in the Applied Sciences. arXiv admin note: text overlap with arXiv:2312.00807