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In the current work we study a nonlocal parabolic problem with Robin boundaryconditions. The problem arises from the study of an idealized electricallyactuated MEMS (Micro-Electro-Mechanical System) device.  Initially we study the steady-state problem in one dimension and we presentsome numerical results regarding its bifurcation diagram. Next the$N-$dimensional nonlocal problem steady-state problem is investigated and aPohozaev-type identity is first obtained which then facilitates derivation ofan estimate of the pull-in voltage for radially symmetric domains. Later thetime-dependent problem is investigated and global-in-time as well as quenchingresults are obtained again for general and radially symmetric domains. We closethe current work with a numerical investigation of the presented nonlocal modelvia an adaptive numerical method. Various numerical experiments are presentedverifying the obtained analytical results.

A study of a nonlocal problem with Robin boundary conditions arising from MEMS technology