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Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS
- Source :
- Journal of Differential Equations 384 (2024), 193 - 251
- Publication Year :
- 2023
-
Abstract
- In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two parallel plates separated by a gas-filled thin gap. The nonlinear parabolic-dispersive coupled system modelling the device consists of a quasilinear parabolic equation for the gas pressure and a semilinear plate equation for gap width. We show the local-in-time existence of strict solutions for the system, by combining a local-in-time existence result for the dispersive equation, H\"{o}lder continuous dependence of its solution on that of the parabolic equation, and then local-in-time existence for a resulting abstract parabolic problem. Semigroup approaches are vital for both main parts of the problem.<br />Comment: 42 pages, 1 figure, to appear in Journal of Differential Equations. arXiv admin note: text overlap with arXiv:2304.14257
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Differential Equations 384 (2024), 193 - 251
- Publication Type :
- Report
- Accession number :
- edsarx.2312.00807
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jde.2023.11.028