Kinetic Boltzmann, Vlasov and Related Equations

Häftad, Engelska, 2011

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Beskrivning

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

Produktinformation

Utgivningsdatum:2011-06-17
Mått:152 x 229 x 17 mm
Vikt:520 g
Format:Häftad
Språk:Engelska
Antal sidor:320
Förlag:Elsevier Science
ISBN:9780323165303

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Fysik inom Naturvetenskap och teknik

Recensioner i media

"...a well-written book, and its topics are carefully chosen and seriously treated. Thus, it is suitable for every researcher or graduate student studying the Boltzmann equation, Vlasov equations, and related equations." --Mathematical Reviews, Kinetic Boltzmann, Vlasov and Related Equations"The reviewed collective monograph presents not only the basics and common facts, but also recent results in the theory of kinetic equations and their many applications." --Zentralblatt MATH 1230-1

Innehållsförteckning

1. Principal Concepts of Kinetic Equations2. Lagrangian Coordinates3. Vlasov-Maxwell and Vlasov-Einstein Equations4. Energetic Substitution5. Introduction in Mathematical Theory of Kinetic Equations6. On the Family of the Steady-State Solutions of Vlasov-Maxwell System7. Boundary Value Problems for the Vlasov-Maxwell System8. Bifurcation of Stationary Solutions of the Vlasov-Maxwell System9. Boltzmann Equation10. Discrete Models of Boltzmann Equation11. Method of Spherical Harmonics and Relaxation of Maxwellian Gas12. Discrete Boltzmann equation Models for Mixtures13. Quantum Hamiltonians and Kinetic Equations14. Modelling of the Limit Problem for the Magnetically Noninsulated Diode15. Generalized Liouville Equation and Approximate Orthogonal Decomposition Methods