Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 01, pp. 1-17.

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

Authors: Michael Kunzinger (Univ.  Wien, Austria)
         Gerhard Rein   (Univ. Bayreuth, Germany)
	 Roland Steinbauer (Univ.  Wien, Austria)
	 Gerald Teschl  (Univ.  Wien, Austria)

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.