A Eigenvalue Problem Of The Linearized Two-Particle Boltzmann Equation System And The Two-Particle Boltzmann H-Theorem

In this paper, firstly we derive the linearized two-particle Boltzmann equation sys-tem. The eigenvalues and eigenfunctions of the integral operator which is derived from the linearized two-particle Boltzmann equation system are obtained.Further more, we prove that the solution of the linearized two-particle Boltzmann equation system decay to equilibrium in time. Secondly, we prove uniqueness of the solution for initial problem of the space homogeneous linearized two-particle Boltzmann equation system. Finally, the definition of H-theorem of two-partical is given and we obtain a Boltzmann H-theorem for two partical.