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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02281 |
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| _version_ | 1866913327038332928 |
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| author | Walker, Christoph |
| author_facet | Walker, Christoph |
| contents | A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the device and the gas pressure. The system is regarded as a special case of a more general setting for which local well-posedness of strong solutions is shown. The general result applies to different cases including a coupling of the parabolic equation to a semilinear wave equation of either second or fourth order, the latter featuring either clamped or pinned boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Quasilinear Parabolic-Hyperbolic System Arising in MEMS Modeling Walker, Christoph Analysis of PDEs A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the device and the gas pressure. The system is regarded as a special case of a more general setting for which local well-posedness of strong solutions is shown. The general result applies to different cases including a coupling of the parabolic equation to a semilinear wave equation of either second or fourth order, the latter featuring either clamped or pinned boundary conditions. |
| title | On a Quasilinear Parabolic-Hyperbolic System Arising in MEMS Modeling |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.02281 |