Kinetic Boltzmann, Vlasov and Related Equations

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Elsevier, Jun 17, 2011 - Mathematics - 320 pages
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Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory.

This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance.



  • Reviews the whole field from the beginning to today
  • Includes practical applications
  • Provides classical and modern (semi-analytical) solutions
 

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Contents

Chapter 1 Principal Concepts of Kinetic Equations
1
Chapter 2 Lagrangian Coordinates
9
Chapter 3 VlasovMaxwell and VlasovEinstein Equations
19
Chapter 4 Energetic Substitution
29
Chapter 5 Introduction to the Mathematical Theory of Kinetic Equations
35
Chapter 6 On the Family of the SteadyState Solutions of VlasovMaxwell System
49
Chapter 7 Boundary Value Problems for the VlasovMaxwell System
69
Chapter 8 Bifurcation of Stationary Solutions of the VlasovMaxwell System
133
Chapter 10 Discrete Models of Boltzmann Equation
183
Chapter 11 Method of Spherical Harmonics and Relaxation of Maxwellian Gas
195
Chapter 12 Discrete Boltzmann Equation Models for Mixtures
211
Chapter 13 Quantum Hamiltonians and Kinetic Equations
227
Chapter 14 Modeling of the Limit Problem for the Magnetically Noninsulated Diode
241
Chapter 15 Generalized Liouville Equation and Approximate Orthogonal Decomposition Methods
261
Glossary of Terms and Symbols
287
Bibliography
289

Chapter 9 Boltzmann Equation
165

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