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Session 13. Global existence versus blowup in nonlinear parabolic systems
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A Free Boundary Problem Modeling Electrostatic MEMS |
Christoph Walker, Leibniz Universität Hannover, Germany
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The talk is based on joint work with Joachim Escher (Hannover) and Philippe Laurençot (Toulouse)
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Idealized microelectromechanical systems (MEMS) consist of a fixed ground plate above which a membrane is suspended deforming due to a voltage difference that is applied between the two components. The mathematical model involves the harmonic electrostatic potential in the free domain between ground plate and membrane along with a singular evolution equation for the membrane displacement, the coupling term being the trace of the potential gradient on the membrane. The number of steady-state solutions and the possible phenomenon of a touchdown of the membrane on the ground plate are analyzed.
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