On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control. (June 2016) - Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.
Abstract: 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.