Abstract
The Bobylev approach to the nonlinear Boltzmann equation is reviewed. The linearized problem is discussed and it is shown that eigenfunctions decaying like a negative power of the velocity are possible with Maxwell molecules only. The relaxation to equilibrium according to the nonlinear equation is discussed and the Krook-Wu conjecture on the status of the BKW mode is shown to be false in general. The buildup of the high-energy tails is considered and a phenomenon observed by Tjon is given a simple explanation. Finally, the method is illustrated with numerical calculations performed for two sets of initial conditions.
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Hauge, E.H., Præstgaard, E. The bobylev approach to the nonlinear Boltzmann equation. J Stat Phys 24, 21–38 (1981). https://doi.org/10.1007/BF01007632
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DOI: https://doi.org/10.1007/BF01007632