  The global-in-time existence of classical solutions to the relativistic
Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after
nearly four decades of mathematical research. In this note, a simplified ``toy
model'' is presented and studied. This toy model retains one crucial aspect of
the RVM system: the phase-space evolution of the distribution function is
governed by a transport equation whose forcing term satisfies a wave equation
with finite speed of propagation.
