Abstract
This paper extends the result of Håkan Andréasson. It's proved that the Cauchy problem for the relativistic Boltzmann equation in a periodic box has a global mild solution if the assumptions of the scattering cross section are weaker than those given by Dudyński and Ekiel-Jezewska and include some hard relativistic interactions, and if the initial distribution function satisfies the conditions that it's periodic in the spacial space and that its mass, energy and entropy are finite in the periodic box.
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