Exact solution of the time-dependent Boltzmann equation for a Lorentz gas

Using the classical methods of mathematical physics one worked out integral solution of the Chapman-Cowling-Davydov equation derived from the Boltzmann kinetic equation with a collision term in the approximation of a Lorentz gas. For a special case of initial distribution the solution is derived in the explicit form. During evolution the distribution function at long (macroscopic) time intervals is determined to approach the Maxwell distribution and not to depend on the exact type of initial distribution. It is consistent with the general concept about the global behavior of nonstationary state of arbitrary isolated system