Analysis of a Model for Electrical Discharge in MEMS
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914350001815552 |
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| author | Gimperlein, Heiko He, Runan Lacey, Andrew A. |
| author_facet | Gimperlein, Heiko He, Runan Lacey, Andrew A. |
| contents | We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as the capacitor's electrodes, one of which is flexible, and which are separated by a narrow gas-filled gap. In the event of the flexible plate approaching the other, electrical discharge can occur. This is modelled here by two parabolic equations, for densities of electrons and positive ions, and an elliptic equation for electric potential. We show the local-in-time existence of a weak solution for the coupled system. Compactness techniques, used previously in the study of drift-diffusion equations, are employed in our proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analysis of a Model for Electrical Discharge in MEMS Gimperlein, Heiko He, Runan Lacey, Andrew A. Analysis of PDEs We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as the capacitor's electrodes, one of which is flexible, and which are separated by a narrow gas-filled gap. In the event of the flexible plate approaching the other, electrical discharge can occur. This is modelled here by two parabolic equations, for densities of electrons and positive ions, and an elliptic equation for electric potential. We show the local-in-time existence of a weak solution for the coupled system. Compactness techniques, used previously in the study of drift-diffusion equations, are employed in our proof. |
| title | Analysis of a Model for Electrical Discharge in MEMS |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.21439 |