Touchdown is the only finite time singularity in a three-dimensional MEMS model

2018/07/24 by Philippe Laurençot, Laurençot, Philippe, Christoph Walker +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1807.09017

arxiv created 2018/07/24 · arxiv updated 2018/07/25

Abstract

Touchdown is shown to be the only possible finite time singularity that may take place in a free boundary problem modeling a three-dimensional microelectromechanical system. The proof relies on the energy structure of the problem and uses smoothing effects of the semigroup generated in L¹ by the bi-Laplacian with clamped boundary conditions.

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