Exponential decay of the linear Maxwell system due to conductivity near the boundary
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917203810451456 |
|---|---|
| author | Nutt, Richard Schnaubelt, Roland |
| author_facet | Nutt, Richard Schnaubelt, Roland |
| contents | We study the anisotropic linear Maxwell system on a bounded domain $Ω$ with perfectly conducting boundary conditions. It is damped via a conductivity $σ$ which is strictly positive on a collar at the boundary. We prove that solutions decay exponentially to 0, if the fields have no magnetic charges on $Ω$ and no electric charges off the support of $σ$. Our approach relies on a splitting of the solution via a Helmholtz decomposition and an observability-type estimate for a related second-order system without charges, shown using Morawetz multipliers. Corresponding exact observability and controllability results are also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential decay of the linear Maxwell system due to conductivity near the boundary Nutt, Richard Schnaubelt, Roland Analysis of PDEs 35Q61 (Primary) 35B35, 35L50, 93B07 (Secondary) We study the anisotropic linear Maxwell system on a bounded domain $Ω$ with perfectly conducting boundary conditions. It is damped via a conductivity $σ$ which is strictly positive on a collar at the boundary. We prove that solutions decay exponentially to 0, if the fields have no magnetic charges on $Ω$ and no electric charges off the support of $σ$. Our approach relies on a splitting of the solution via a Helmholtz decomposition and an observability-type estimate for a related second-order system without charges, shown using Morawetz multipliers. Corresponding exact observability and controllability results are also established. |
| title | Exponential decay of the linear Maxwell system due to conductivity near the boundary |
| topic | Analysis of PDEs 35Q61 (Primary) 35B35, 35L50, 93B07 (Secondary) |
| url | https://arxiv.org/abs/2601.09502 |