• On the quenching behaviour of a semilinear wave equation modelling MEMS technology

      Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.; Tzanetis, Dimitrios E.; University of Chester ; Heriot-Watt University ; University of Aegean ; National Technical University of Athens (American Institute of Mathematical Sciences, 2014-10-01)
    • On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control

      Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.; University of Chester; Heriot-Watt University; University of Aegean (Elsevier, 2016-02-28)
      We consider a nonlocal parabolic model for a micro-electro-mechanical system. Specifically, for a radially symmetric problem with monotonic initial data, it is shown that the solution quenches, so that touchdown occurs in the device, in a situation where there is no steady state. It is also shown that quenching occurs at a single point and a bound on the approach to touchdown is obtained. Numerical simulations illustrating the results are given.