2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98253We consider a collisionless ensemble of classical particles coupled to 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.18 pages, LaTeXAnalysis of PDEsMathematical Physics35A07; 35Q72; 35Q40; 82C22text