
Author(s)  Cercignani, Carlo 

Title  Mathematical Methods in Kinetic Theory (Second Ed.) 
Publisher  Plenum Press 
Year of publication  1990 
Reviewed by  VALERII V. TROFIMOV 
There are now a greater range of mathematical treatments used in theoretical physics than ever. The aim of Mathematical Methods in Kinetic Theory is the boundary value problems arising in connection with the Boltzmann equation, which has the form <formula> with unknown function P(t, x) of probability density, where <formula> is velocity vector of ith particle (i = 1, ..., N) of the system. The basic properties of the Boltzmann equation is studied. The exact solution of this equation is constructed, this is the Maxwellian. Bhatnagar, Gross, and Krook nonlinear model as well as the linearized Boltzmann equation are presented here in detail. Methods of solving for the Boltzmann equation based on perturbation expansions are elucidated.
It is worthy of note that there are not the book of this type. Contrary to the usual books on statistical physics, the book under review contains the mathematical methods rather than results.
The rough contents are as follows: Basic Principles, Basic Properties, The Linearized Collision Operator, Model Equation, The Hilbert and ChapmanEnskog Theories, Basic Results on the Solutions of the Boltzmann Equation, Analitical Methods of Solution, Other Methods of Solution, Author Index, Subject Index.
The level is the postgraduate students in theoretical physics. The important prerequisite results of the theory of generalized functions are discussed.
All in all, Mathematical Methods in Kinetic Theory is wellwritten introduction to the kinetic theory of gases and nontrivial mathematics used in the statistical theory of the dynamics of mechanical systems with large degrees of freedom. The purchase of this book is a good investment for both physicists and applied mathematicians. The libraries have to have this book alike.