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.
|Number of pages||18|
|Journal||Nonlinear Analysis: Theory, Methods and Applications|
|Early online date||28 Feb 2016|
|Publication status||Published - Jun 2016|
- Electrostatic MEMS
Lacey, A. A., Kavallaris, N., & Nikolopoulos, C. (2016). On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control. Nonlinear Analysis: Theory, Methods and Applications, 138, 189–206. https://doi.org/10.1016/j.na.2016.02.001