  We establish the global-in-time existence and uniqueness of classical
solutions to the "one and one-half" dimensional relativistic Vlasov--Maxwell
systems in a bounded interval, subject to an external magnetic field which is
infinitely large at the spatial boundary. We prove that the large external
magnetic field confines the particles to a compact set away from the boundary.
This excludes the known singularities that typically occur due to particles
that repeatedly bounce off the boundary. In addition to the confinement, we
follow the techniques introduced by Glassey and Schaeffer, who studied the
Cauchy problem without boundaries.

Analysis of PDEs