Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915729777885184 |
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| author | Nutt, Richard Schnaubelt, Roland |
| author_facet | Nutt, Richard Schnaubelt, Roland |
| contents | We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding non-autonomous linear problem, an observability-type estimate, and a detailed regularity analysis. The results are improved in the linear autonomous case, using properties of the Helmholtz decomposition in Sobolev spaces of (small) negative order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary Nutt, Richard Schnaubelt, Roland Analysis of PDEs 35Q61 (Primary) 35L50, 35B40, 35B65 (Secondary) We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding non-autonomous linear problem, an observability-type estimate, and a detailed regularity analysis. The results are improved in the linear autonomous case, using properties of the Helmholtz decomposition in Sobolev spaces of (small) negative order. |
| title | Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary |
| topic | Analysis of PDEs 35Q61 (Primary) 35L50, 35B40, 35B65 (Secondary) |
| url | https://arxiv.org/abs/2601.09490 |