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On a free boundary model for three-dimensional MEMS with a hinged top plate II: Parabolic case

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  • A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a fourth-order semilinear parabolic equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the device. The strength of the coupling is tuned by a parameter $ \lambda $ which is proportional to the square of the applied voltage difference. It is proven that the model is locally well-posed in time and that, for $ \lambda $ sufficiently small, solutions exist globally in time. In addition, touchdown of the top plate on the ground plate is shown to be the only possible finite time singularity.

    Mathematics Subject Classification: 35K91, 35R35, 35M33, 35Q74, 35B44.


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  • Figure 1.  Cross section of the idealized MEMS device

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