Electron. J. Diff. Eqns., Vol. 2005(2005), No. 01, pp. 1-17.

On classical solutions of the relativistic Vlasov-Klein-Gordon system

Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl

Abstract:
We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.

Submitted October 12, 2004. Published January 2, 2005.
Math Subject Classifications: 35A07, 35Q72, 35Q40, 82C22.
Key Words: Vlasov equation; Klein-Gordon equation; classical solutions.

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Michael Kunzinger
Fakultät für Mathematik, Universität Wien
Nordbergstrasse 15
1090 Wien, Austria
email: Michael.Kunzinger@univie.ac.at
http://www.mat.univie.ac.at/~mike
Gerhard Rein
Fakultät für Mathematik und Physik
Universität Bayreuth
95440 Bayreuth, Germany
email: gerhard.rein@uni-bayreuth.de
http://www.uni-bayreuth.de/departments/math/org/mathe6/staff/memb/grein/home.html
Roland Steinbauer
Fakultät für Mathematik, Universität Wien
Nordbergstrasse 15
1090 Wien, Austria
email: Roland.Steinbauer@univie.ac.at
http://www.mat.univie.ac.at/~stein/
Gerald Teschl
Fakultät für Mathematik, Universität Wien
Nordbergstrasse 15
1090 Wien, Austria
email: Gerald.Teschl@univie.ac.at
http://www.mat.univie.ac.at/~gerald/

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