On a nonlocal parabolic problem arising in electrostatic MEMS control
Jong‐Shenq Guo, Nikos I. Kavallaris · Discrete and Continuous Dynamical Systems · 2012
We consider a nonlocal parabolic equation associated with Dirichlet boundary and initial conditions arising in MEMS control.First, we investigate the structure of the associated steady-state problem for a general star-shaped domain.Then we classify radially symmetric stationary solutions and their radial Morse indices.Finally, we study under which circumstances the solution of the time-dependent problem is global-in-timeor quenches in finite time.