In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), anewnon-linearsecond-orderdifferentialmodelwithsingularityinthesteady-statecaseispresented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.
A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness / Di Barba, Paolo; Fattorusso, Luisa Angela Maria; Versaci, Mario. - In: MATHEMATICS. - ISSN 2227-7390. - 7:12(2019), pp. 1-18. [10.3390/math7121193]
A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness
Luisa Fattorusso;Mario Versaci
2019-01-01
Abstract
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), anewnon-linearsecond-orderdifferentialmodelwithsingularityinthesteady-statecaseispresented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.| File | Dimensione | Formato | |
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