Qualitative behavior of nonlinear Maxwell equations (A05)

• Subject Area: Mathematics
• Term: since 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

Maxwell equations are the fundamental laws governing electromagnetic theory. In the case of nonlinear material laws, they pose many challenging mathematical problems. For instantaneous or retarded laws, we develop a wellposedness theory and look for sufficient conditions for global-in-time existence. We also study convergence to 0 and the long-time behavior near special solutions. Core tools are dispersive estimates and energy methods.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Professor Dr. Roland Schnaubelt; Professor Dr. Lutz Weis, until 6/2019