  In the current work we study a nonlocal parabolic problem with Robin boundary
conditions. The problem arises from the study of an idealized electrically
actuated MEMS (Micro-Electro-Mechanical System) device.
  Initially we study the steady-state problem in one dimension and we present
some numerical results regarding its bifurcation diagram. Next the
$N-$dimensional nonlocal problem steady-state problem is investigated and a
Pohozaev-type identity is first obtained which then facilitates derivation of
an estimate of the pull-in voltage for radially symmetric domains. Later the
time-dependent problem is investigated and global-in-time as well as quenching
results are obtained again for general and radially symmetric domains. We close
the current work with a numerical investigation of the presented nonlocal model
via an adaptive numerical method. Various numerical experiments are presented
verifying the obtained analytical results.
