Electron. J. Differential Equations, Vol. 2018 (2018), No. 73, pp. 1-9.

Blow-up for nonlinear Maxwell equations

Piero D'Ancona, Serge Nicaise, Roland Schnaubelt

We construct classical solutions to the nonlinear Maxwell system with periodic boundary conditions which blow up in H(curl). A similar result is shown on the full space. Our construction is based on an analysis of a shock wave in one space dimension.

Submitted March 15, 2017. Published March 15, 2018.
Math Subject Classifications: 35L60, 35Q61.
Key Words: Quasilinear Maxwell system; blow-up; shock; Kerr model.

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  Piero D'Ancona
Dipartimento di Matematica
Sapienza Unversità di Roma
Piazzale A.~Moro 2, 00185 Roma, Italy
email: dancona@mat.uniroma1.it
Serge Nicaise
Université de Valenciennes
EA 4015 - LAMAV - FR CNRS 2956
F-59313 Valenciennes, France
email: serge.nicaise@univ-valenciennes.fr
Roland Schnaubelt
Department of Mathematics
Karlsruhe Institute of Technology
76128 Karlsruhe, Germany
email: schnaubelt@kit.edu

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