2021/03/11 by Katerina Nik, Nik, Katerina
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2103.06776
openalex publication_date 2021/03/11 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A parabolic free boundary problem modeling a three-dimensional electrostatic\nMEMS device is investigated. The device is made of a rigid ground plate and an\nelastic top plate which is hinged at its boundary, the plates being held at\ndifferent voltages. The model couples a fourth-order semilinear parabolic\nequation for the deformation of the top plate to a Laplace equation for the\nelectrostatic potential in the device. The strength of the coupling is tuned by\na parameter \λ which is proportional to the square of the applied\nvoltage difference. It is proven that the model is locally well-posed in time\nand that, for \λ sufficiently small, solutions exist globally in time.\nIn addition, touchdown of the top plate on the ground plate is shown to be the\nonly possible finite time singularity.\n