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Bobylev, A.V., Cercignani, C. and Toscani, G. (2003) Proof of an Asymptotic Property of Self-Similar Solutions of the Boltzmann Equation for Granular Materials. Journal of Statistical Physics, 111, 403-417.
https://doi.org/10.1023/A:1022273528296

has been cited by the following article:

• TITLE: The Existence of Solutions of a Space-Uniform Boltzmann Equation

  AUTHORS: Zhihui Ye, Rulv Li

  KEYWORDS: Space-Uniform Boltzmann Equations, Self-Mapping, Contractive Mapping, Uniformly Bounded, The Existence of the Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.2, February 12, 2020

  ABSTRACT: Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.