Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical Aspects of the Theory

Discrete velocity models of the Boltzmann equation are of considerable conceptual interest in the kinetic theory of gases, and, at the same time, a fascinating mathematical subject. The last decade has seen a lot of work on this subject, which is reviewed here. We put an emphasis on mathematical asp...

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Published inSIAM review Vol. 30; no. 2; pp. 213 - 255
Main Authors Platkowski, Tadeusz, Illner, Reinhard
Format Journal Article
LanguageEnglish
Published Philadelphia The Society for Industrial and Applied Mathematics 01.06.1988
Society for Industrial and Applied Mathematics
Subjects
Applied mathematics
Boltzmann equation
Cauchy problem
Existence theorems
Flow velocity
Gases
Kinetic theory
Mathematical models
Mathematical problems
Particle collisions
Semigroups
Velocity
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Summary:Discrete velocity models of the Boltzmann equation are of considerable conceptual interest in the kinetic theory of gases, and, at the same time, a fascinating mathematical subject. The last decade has seen a lot of work on this subject, which is reviewed here. We put an emphasis on mathematical aspects, in particular the global existence question, qualitative properties of solutions, explicit solutions, and the fluid dynamical limit. The mechanical background is discussed more concisely in Part I. Numerous contributions concerning other questions are outlined. We try to give a complete reference list up to and including 1985.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1445
1095-7200
DOI:10.1137/1030045