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Touchdown and related problems in electrostatic MEMS device equation

Nonlinear Differential Equations and Applications (2008) 15(3) 363-385
DOI: 10.1007/s00030-008-7081-5
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Abstract

We study the electrostatic MEMS-device equation, ut - Δu = λ|x|β/(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. © 2008 Birkhaueser.

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Kavallaris, N. I., Miyasita, T., & Suzuki, T. (2008). Touchdown and related problems in electrostatic MEMS device equation. Nonlinear Differential Equations and Applications, 15(3), 363–385. https://doi.org/10.1007/s00030-008-7081-5

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