Electron. J. Differential Equations 2005, No. 01, 1-17 (2005) [url]

On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System

Michael Kunzinger, Gerhard Rein, Roland Steinbauer, and Gerald Teschl

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.

MSC2000: 35A07, 35Q72, 35Q40, 82C22
Keywords: Vlasov equation; Klein-Gordon equation; classical solutions

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