Initial-boundary problem for the 1-D Euler-Boltzmann equations in radiation hydrodynamics

We study the initial-boundary value problem for the one dimensional Euler-Boltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified Glimm scheme to construct the global approximate solutions (UΔt,d, IΔt,d) and prove that there is a subsequence of the approximate solutions which is convergent to the global solution.