Piero D'Ancona, Serge Nicaise, Roland Schnaubelt
Abstract:
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 | |
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Serge Nicaise Université de Valenciennes EA 4015 - LAMAV - FR CNRS 2956 F-59313 Valenciennes, France email: serge.nicaise@univ-valenciennes.fr |
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Roland Schnaubelt Department of Mathematics Karlsruhe Institute of Technology 76128 Karlsruhe, Germany email: schnaubelt@kit.edu |
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