The Boltzmann equation and corresponding extremal problems

الأصل · EN

We start with some global Maxwellian function M, which is a stationary solution (with the constant total density ρ) of the Boltzmann equation, and we denote the number of the corresponding space variables by n. The notion of distance between the global Maxwellian function and an arbitrary solution f (with the same total density ρ at the fixed moment t) of the Boltzmann equation is introduced. In this way we essentially generalize the important Kullback-Leibler distance, which was used before. An extremal problem to find a solution of the Boltzmann equation, such that {M,f} is minimal in the class of solutions with the fixed values of energy and of n moments, is solved.