| Abstract: |
| Qualitative properties of solutions to the evolution problem modelling
microelectromechanical systems (MEMS) with general permittivity profile are
investigated. The system couples a parabolic evolution problem for
the displacement of a membrane with an elliptic free boundary value problem
for the electric potential in the region between the membrane and a rigid
ground plate. Conditions are specified which ensure the non-positivity
of the membrane`s displacement. Moreover, assuming to have a
non-positive displacement, it is shown that the solution develops a
singularity after a finite time of existence. |
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