Geodesic
On classical solutions of the relativistic Vlasov-Klein-Gordon system
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 35A07, 35Q72, 35Q40, 82C22
Keywords: Vlasov equation, Klein-Gordon equation, classical solutions 
@article{EJDE_2005__2005__a52,
     author = {Kunzinger,  Michael and Rein,  Gerhard and Steinbauer,  Roland and Teschl,  Gerald},
     title = {On classical solutions of the relativistic {Vlasov-Klein-Gordon} system},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1080.35162},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a52/}
}
TY  - JOUR
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AU  - Rein,  Gerhard
AU  - Steinbauer,  Roland
AU  - Teschl,  Gerald
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JO  - Electronic journal of differential equations
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VL  - 2005
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LA  - en
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%A Steinbauer,  Roland
%A Teschl,  Gerald
%T On classical solutions of the relativistic Vlasov-Klein-Gordon system
%J Electronic journal of differential equations
%D 2005
%V 2005
%U http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a52/
%G en
%F EJDE_2005__2005__a52
Kunzinger,  Michael; Rein,  Gerhard; Steinbauer,  Roland; Teschl,  Gerald. On classical solutions of the relativistic Vlasov-Klein-Gordon system. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a52/