  In this paper, we study the global wellposedness of a radiation hydrodynamics
model with viscosity and thermal conductivity. It is now well-understood that,
unlike the compressible Euler equations whose smooth solutions must blow up in
finite time no matter how small and how smooth the initial data is, the
dissipative structure of such a radiation hydrodynamics model can indeed
guarantee that its one-dimensional Cauchy problem admits a unique global smooth
solution provided that the initial data is sufficiently small, while for large
initial data, even if the heat conductivity is taken into account but the
viscosity effect is ignored, shock type singularities must appear in finite
time for smooth solutions of the Cauchy problem of one-dimensional radiation
hydrodynamics model with thermal conductivity and zero viscosity. Thus a
natural question is, if effects of both the viscosity and the thermal
conductivity are considered, does the one-dimensional radiation hydrodynamics
model with viscosity and thermal conductivity exist a unique global large
solution? We give an affirmative answer to this problem and show in this paper
that the initial-boundary value problem to the radiation hydrodynamics model in
an one-dimensional periodic box T = R/Z with viscosity and thermal conductivity
does exist a unique global smooth solution for any large initial data. The main
ingredient in our analysis is to introduce some delicate estimates, especially
an improved estimate on the absolute temperature and a pointwise estimate
between the absolute temperature, the specific volume, and the first-order
spatial derivative of the macro radiation flux, to deduce the desired positive
lower and upper bounds on the density and the absolute temperature.
