Springfield: American Institute of Mathematical Sciences
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-time or quenches in finite time.
Discrete and Continuous Dynamical Systems 32(5), pp.1723-1746