# American Institute of Mathematical Sciences

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## Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties

 1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, F–31062 Toulouse Cedex 9, France 2 Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D–30167 Hannover, Germany

* Corresponding author

Dedicated to Michel Pierre on the occasion of his 70th birthday

Received  October 2019 Published  May 2020

Fund Project: Partially supported by the CNRS Projet International de Coopération Scientifique PICS07710

The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with heterogeneous dielectric properties.

Citation: Philippe Laurençot, Christoph Walker. Variational solutions to an evolution model for MEMS with heterogeneous dielectric properties. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020360
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Geometry of $\Omega(u)$ for a state $u = v$ with empty coincidence set (green)
Geometry of $\Omega(u)$ for a state $u = w$ with non-empty coincidence set (blue)