Wellposedness of an elliptic-dispersive coupled system for MEMS

Heiko Gimperlein*, Runan He, Andrew A. Lacey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this work, we study the local wellposedness of the solution to a nonlinear elliptic-dispersive coupled system which serves as a model for a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device consists of two parallel plates separated by a gas-filled thin gap. The nonlinear elliptic-dispersive coupled system modelling the device combines a linear elliptic equation for the gas pressure with a semilinear dispersive equation for the gap width. We show the local-in-time existence of strict solutions for the system, by combining elliptic regularity results for the elliptic equation, Lipschitz continuous dependence of its solution on that of the dispersive equation, and then local-in-time existence for a resulting abstract dispersive problem. Semigroup approaches are key to solve the abstract dispersive problem.

Original languageEnglish
Pages (from-to)3485-3511
Number of pages27
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number9
Early online date1 May 2023
Publication statusPublished - Sept 2023


  • Elliptic-dispersive coupled system
  • local wellposedness
  • MEMS
  • semigroup theory
  • solid-plate thin-film-flow interactions

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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