Kinetic Boltzmann, Vlasov and Related Equations
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.
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Chapter 5 Introduction to the Mathematical Theory of Kinetic Equations
Chapter 6 On the Family of the SteadyState Solutions of VlasovMaxwell System
Chapter 7 Boundary Value Problems for the VlasovMaxwell System
Chapter 8 Bifurcation of Stationary Solutions of the VlasovMaxwell System
Chapter 10 Discrete Models of Boltzmann Equation
Chapter 11 Method of Spherical Harmonics and Relaxation of Maxwellian Gas
Chapter 12 Discrete Boltzmann Equation Models for Mixtures
Chapter 13 Quantum Hamiltonians and Kinetic Equations
Chapter 14 Modeling of the Limit Problem for the Magnetically Noninsulated Diode
Chapter 15 Generalized Liouville Equation and Approximate Orthogonal Decomposition Methods
Glossary of Terms and Symbols
Chapter 9 Boltzmann Equation