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On the quenching behaviour of a semilinear wave equation modelling MEMS technology
University of Chester, GBR.ORCID iD: 0000-0002-9743-8636
Heriot-Watt University, GBR.
University of the Aegean, GRC.
National Technical University of Athens, GRC.
2015 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 35, no 3, p. 1009-1037Article in journal (Refereed) Published
Abstract [en]

In this work we study the semilinear wave equation of the form u tt = u xx + λ/(1 − u) 2 , with homogeneous Dirichlet boundary conditions and suitable initial conditions, which, under appropriate circumstances, serves as a model of an idealized electrostatically actu-ated MEMS device. First we establish local existence of the solutions of the problem for any λ > 0. Then we focus on the singular behaviour of the solution, which occurs through finite-time quenching, i.e. when ||u(·, t)|| ∞ → 1 as t → t * − < ∞, investigating both conditions for quenching and the quenching profile of u. To this end, the non-existence of a regular similarity solution near a quenching point is first shown and then a formal asymptotic expansion is used to determine the local form of the solution. Finally, using a finite difference scheme, we solve the problem numerically, illustrating the preceding results.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2015. Vol. 35, no 3, p. 1009-1037
Keywords [en]
Electrostatic MEMS, quenching of solution, hyperbolic problems, formal asymptotic, similarity analysis.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88599DOI: 10.3934/dcds.2015.35.1009ISI: 000344577500013Scopus ID: 2-s2.0-84908227591OAI: oai:DiVA.org:kau-88599DiVA, id: diva2:1638697
Available from: 2022-02-17 Created: 2022-02-17 Last updated: 2022-11-21Bibliographically approved

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Kavallaris, Nikos I.

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  • apa
  • ieee
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  • apa.csl
  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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