Geodesic
On classical solutions of the relativistic Vlasov-Klein-Gordon system
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a52/}
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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/