Abstract.
We study the electrostatic MEMS-device equation, \(u_{t} -\Delta u = \frac{\lambda |x|^{\beta}}{(1-u)^{p}}\), with Dirichlet boundary condition. First, we describe the touchdown of non-stationary solution in accordance with the total set of stationary solutions. Then, we classify radially symmetric stationary solutions and their radial Morse indices. Finally, we show the Morse-Smale property for radially symmetric non-stationary solutions.
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On leave to Department of Statistics and Actuarial Science, University of the Aegean, current email address:nkaval@aegean.gr
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Kavallaris, N.I., Miyasita, T. & Suzuki, T. Touchdown and related problems in electrostatic MEMS device equation. Nonlinear differ. equ. appl. 15, 363–386 (2008). https://doi.org/10.1007/s00030-008-7081-5
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DOI: https://doi.org/10.1007/s00030-008-7081-5