  We investigate the large-time behavior of solutions toward the combination of
the boundary layer and 3-rarefaction waves to the outflow problem for the
compressible non-isentropic Navier-Stokes equations coupling with the Maxwell
equations through the Lorentz force (called the Navier-Stokes-Maxwell
equations) on the half line $ \mathbb{R}_+ $. It includes the electrodynamic
effects into the dissipative structure of the hyperbolic-parabolic system and
turns out to be more complicated than that in the simpler compressible
Navier-Stokes equations. We prove that this typical composite wave pattern is
time-asymptotically stable with the composite boundary condition of the
electromagnetic fields, under some smallness conditions and the assumption that
the dielectric constant is bounded. This can be viewed as the first result
about the nonlinear stability of the combination of two different wave patterns
for the IBVP of the non-isentropic Navier-Stokes-Maxwell equations.
