Normal trace inequalities and decay of solutions to the nonlinear Maxwell equations with absorbing boundary
Abstract:
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 linear problem and a observability-type estimate and a detailed regularity analysis
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 11.2022 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000153101 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 24 S. |
| Serie | CRC 1173 Preprint ; 2022/63 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | Quasilinear Maxwell system, absorbing boundary conditions, nonhomogenous anisotropic materials, trace regularity, exponential decay |