Nonlinear Maxwell Equations (Winter Semester 2019/20)
- Lecturer: Prof. Dr. Roland Schnaubelt
- Classes: Lecture (0105360), Problem class (0105370)
- Weekly hours: 4+2
- Audience: Mathematics (from 7. semester)
Unfortunately the exercise classes have to be cancelled. Please note that several lectures will be moved to the time slot of the exercises.
The lecture of 16 January will be moved to 15 January at 11:30 in SR 2.59.
|Lecture:||Tuesday 9:45-11:15||SR 3.69||Begin: 15.10.2019|
|Thursday 9:45-11:15||SR 3.61|
|Problem class:||Wednesday 8:00-9:30||SR 2.58||Begin: 16.10.2019|
|Lecturer||Prof. Dr. Roland Schnaubelt|
|Office hours: Wednesday, 11:30 - 13:00, and by appointment|
|Room 2-047 (Englerstr. 2) Kollegiengebäude Mathematik (20.30)|
The Maxwell equations are the fundamental laws governing electro-magnetic phenomena. Constitutive relations describe the interaction between the fields and the material by determining the polarization or magnetization. We study nonlinear relations focussing on an instantaneous material response. The Maxwell system then becomes a quasilinear hyperbolic system. We first investigate the full space case. Here one can establish local wellposedness for initial values in H^3 by well-established energy methods. Problems on domains with boundary conditions (or interface problems) are much more demanding. We present very recent results and discuss the strategy of proof. We will further study blow-up phenomena and decay properties in the presence of an conductivity.
The lectures requires knowledge in functional analysis and basics of Sobolev spaces. Further tools will be discussed in the lectures, possibly without giving complete proofs.
There is an oral exam of about 30 min (for 8 ECTS points).
- S. Benzoni-Gavage and D. Serre: Multidimensional Hyperbolic Partial Differential Equations.
- M. Cessenat: Mathematical Methods in Electromagnetism.