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The relativistic Boltzmann equation in bounded domains has been widely usedin physics and engineering, for example, Tokamak devices in fusion reactors.Inspite of its importance, there has, to the best of our knowledge, been nomathematical theory on the global existence of solutions to the relativisticBoltzmann equation in bounded domains. In the present paper, assuming that themotion of single-species relativistic particles in a bounded domain is governedby the relativistic Boltzmann equation with diffuse reflection boundaryconditions of non-isothermal wall temperature of small variations around apositive constant, and regarding the speed of light $\mathfrak{c}$ as a largeparameter, we first construct a unique non-negative stationary solution$F_{*}$, and further establish the dynamical stability of such stationarysolution with exponential time decay rate. We point out that the$L^{\infty}$-bound of perturbations for both steady and non-steady solutionsare independent of the speed of light $\mathfrak{c}$, and such uniform in$\mathfrak{c}$ estimates will be useful in the study of Newtonian limit in thefuture.

The Global Well-Posedness of the Relativistic Boltzmann Equation with Diffuse Reflection Boundary Condition in Bounded Domains