NO TOUCHDOWN AT POINTS OF SMALL PERMITTIVITY AND NONTRIVIAL TOUCHDOWN SETS FOR THE MEMS PROBLEM

摘要

We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, involving a parabolic equation with singular nonlinearity. We study the touchdown, or quenching, phenomenon. Recently, the question whether or not touchdown can occur at zero points of the permittivity profile f, which had long remained open, was answered negatively for the case of interior points.