Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties

Touchdown and related problems in electrostatic MEMS device equation

“…Kaplan's method could be also used to prove touchdown for big enough λ, see [11]. Now, we show the first case of Theorem 1.1, i.e., λ > λ implies (1.2).…”

“…The structure of the set of stationary solutions has been studied for p = 2 ( [8,11]). We obtain, similarly, an upper bound of λ for the existence of the solution denoted by λ > 0 for general p > 1.…”

On the partial differential equations of electrostatic MEMS devices II: Dynamic case

“…A mathematical model of the physical phenomena, leading to a partial differential equation for the dimensionless dynamic deflection of the membrane, was derived and analyzed in [7] and [11]. In the damping-dominated limit, and using a narrow-gap asymptotic analysis, the dimensionless dynamic deflection u = u(x, t) of the membrane on a bounded domain Ω in R N , is found to satisfy the following Vol.…”

Similarity: generalizations, applications and open problems

“…[24,25]), and quenching behaviour in a nonlinear PDE model of a MEMS capacitor (cf. [26]). For such problems, a singularity forms in finite time whereby either the solution or its partial derivatives diverge.…”