Existence and uniqueness for a coupled parabolic-hyperbolic model of MEMS

Heiko Gimperlein*, Runan He, Andrew A. Lacey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
16 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)6310-6353
Number of pages44
JournalMathematical Methods in the Applied Sciences
Issue number7
Early online date30 Jan 2024
Publication statusPublished - 15 May 2024


  • local wellposedness
  • membrane thin-film-flow interactions
  • MEMS
  • parabolic-hyperbolic coupled system
  • semigroup theory

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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