Wellposedness of a nonlinear parabolic-dispersive coupled system modelling MEMS

Heiko Gimperlein, Runan He, Andrew A. Lacey

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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, Hölder 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.
Original languageEnglish
Pages (from-to)193-251
Number of pages59
JournalJournal of Differential Equations
Volume384
Early online date5 Dec 2023
DOIs
Publication statusE-pub ahead of print - 5 Dec 2023

Keywords

  • Local wellposedness
  • MEMS
  • Parabolic-dispersive coupled system
  • Semigroup theory
  • Solid-plate thin-film-flow interactions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this