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A study of a nonlocal problem with Robin boundary conditions arising from technology
University of Aegean, GRC.
University of Chester, GBR.ORCID iD: 0000-0002-9743-8636
University of Aegean, GRC.
2021 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 44, no 13, p. 10084-10120Article in journal (Refereed) Published
Abstract [en]

In the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro-electro-mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady-state problem is investigated estimates of the pull-in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull-in voltage for radially symmetric N-dimensional domains. Next a detailed study of the time-dependent problem is delivered and global-in-time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2021. Vol. 44, no 13, p. 10084-10120
Keywords [en]
electrostatic MEMS; non-local parabolic problems; Pohožaev's identity; quenching; touchdown
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88690DOI: 10.1002/mma.7393ISI: 000646655300001Scopus ID: 2-s2.0-85104997553OAI: oai:DiVA.org:kau-88690DiVA, id: diva2:1639894
Available from: 2022-02-22 Created: 2022-02-22 Last updated: 2022-03-31Bibliographically approved

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Kavallaris, Nikos I.

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • apa.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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