Abstract
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential threshold is not accompanied by a break-down of the model, but is recovered by the saturation of the constraint for pulled-in states. It is shown that a maximal stationary solution exists and that saturation only occurs for large potential values. In addition, the existence, uniqueness, and large time behavior of solutions to the evolution equation are studied.
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Part of this work was done while PhL enjoyed the hospitality and support of the Institut für Angewandte Mathematik, Leibniz Universität Hannover.
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Partially supported by the CNRS Project PICS07710.
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Laurençot, P., Walker, C. A constrained model for MEMS with varying dielectric properties. J Elliptic Parabol Equ 3, 15–51 (2017). https://doi.org/10.1007/s41808-017-0003-0
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DOI: https://doi.org/10.1007/s41808-017-0003-0