Abstract
The Boltzmann equation is a nonlinear integro-differential equation not solvable in a closed analytical form for realistic potential models. Therefore the Boltzmann equation and the generic Boltzmann equation in general must be solved by an approximation method. To prepare ourselves for approximate solutions, for a class of approximation methods, and for the nonequilibrium ensemble method we discuss some mathematical tools used in developing the theory intended in this work. The discussion will be confined only to what is needed for our aim.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Grad, Comm. Pure Appl. Math. 2, 325 (1949).
B. C. Eu and Y. G. Ohr, Physica A 202, 321 (1994).
A. Erdelyi, ed., Higher Transcendental Functions (H. Bateman Manuscripts) (McGraw-Hill, New York, 1953), Vol. 2, pp. 283–291.
P. M. Morse and H. Feshbach, Methods of Mathematical Physics (McGraw-Hill, New York, 1953 ), Vol. 1, p. 786.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Eu, B.C. (1998). Mathematical Preparation. In: Nonequilibrium Statistical Mechanics. Fundamental Theories of Physics, vol 93. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2438-8_5
Download citation
DOI: https://doi.org/10.1007/978-94-017-2438-8_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5007-6
Online ISBN: 978-94-017-2438-8
eBook Packages: Springer Book Archive