In the first part of the paper it is shown, that in the case of specific initial conditions, solutions of the Cauchy problem for linearized Boltzmann equation have exponential damping when time tends to infinity. In the second part of the paper exact analytic solution of spatially homogeneous linearized Boltzmann equation is built by the use of discrete Laplace transform. The result may be useful in research tasks inside the area of applied rarefied gas dynamics.
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