4 problems

Stability and quenching-profile conjecture. The following statements are conjectured:

Attainability conjecture.

Consider the typical MEMS problem with spatially dependent coefficient $|x|^m$, whose solution $u$ has quenching set $\mathcal{Q}$; a point is a quenching point if it is approached…

Let $T$ denote the finite quenching time of the solution of the MEMS equation with fringing parameter $\delta>0$ and voltage parameter $\lambda>\lambda_\delta^*$, where…