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On a nonlocal parabolic problem arising in electrostatic MEMS control

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  • 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.
    Mathematics Subject Classification: Primary: 35K55, 35J60; Secondary: 74H35, 74G55, 74K15.


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