The Boltzmann Equation as a Physical and Mathematical Model

Abstract

The purpose of this chapter is to present the main mathematical and physical notions related to the kinetic Boltzmann equation and to give some formulae of the kinetic apparatus. Questions concerning the frameworks of the validity of this equation are not discussed. Neither do we consider the interesting problems of derivation of the kinetic equation nor its connection with the Liouville equation. Minimum information will be presented about the basic kinetic theory points, binary collisions, and molecular models. The aim of Chapter 1 to provide the mathematical tools which are needed to deal (analytically or numerically) with the Boltzmann equation. The peculiarities of formulation of mathematical problems for the kinetic equation and some types of the boundary conditions are considered. The physical peculiarities of the kinetic Boltzmann equation (in particular, the important property of irreversibility) are also discussed.