Quenching for a semi-linear wave equation for micro-electro-mechanical systems

Heiko Gimperlein*, Runan He, Andrew A. Lacey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
15 Downloads (Pure)

Abstract

We consider the formation of finite-time quenching singularities for solutions of semi-linear wave equations with negative power nonlinearities, such as can model micro-electro-mechanical systems. For radial initial data we obtain, formally, the existence of a sequence of quenching self-similar solutions. Also from formal aymptotic analysis, a solution to the PDE which is radially symmetric and increases strictly monotonically with distance from the origin quenches at the origin like an explicit spatially independent solution. The latter analysis and numerical experiments suggest a detailed conjecture for the singular behaviour.

Original languageEnglish
Article number20220490
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume478
Issue number2267
DOIs
Publication statusPublished - 30 Nov 2022

Keywords

  • finite-time singularities
  • micro-electro-mechanical systems
  • quenching
  • self-similar solution
  • semi-linear wave equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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