Local wellposedness of Maxwell systems with scalar-type retarded material laws
Abstract:
We study the local wellposedness in $H^2$ for the system of Maxwell equations in a bounded domain equipped with perfectly conducting boundary conditions. The medium is described by a retarded and nonlinear expression for the polarisation having the property that the polarisation is always parallel to the electricfield. An example is the Kerr effect in a homogeneous, isotropic and inversion-symmetric medium. The results are obtained using semigroup theory.
| 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: 1000153335 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 71 S. |
| Serie | CRC 1173 Preprint ; 2022/68 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | Nonlinear Maxwell equations, retarded material laws, perfectly conducting boundary conditions, local wellposedness, retarded evolution equations |