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.