Kinetic Boltzmann, Vlasov and related equations /
Sinitsyn, Alexander.
Dulov, Eugene.
Vedenyapin, Victor(Victor Valentinovich),1949-
Waltham, Mass. : Elsevier Science,
2011.
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.
Includes bibliographical references (p. [289]-304).
Principal Concepts of Kinetic Equations -- 2. Lagrangian Coordinates -- 3. Vlasov-Maxwell and Vlasov-Einstein Equations -- 4. Energetic Substitution -- 5. Introduction to the Mathematical Theory of Kinetic Equations -- 6. On the Family of the Steady-State Solutions of Vlasov-Maxwell System -- 7. Boundary Value Problems for the Vlasov-Maxwell System -- 8. Bifurcation of Stationary Solutions of the Vlasov-Maxwell System -- 9. Boltzmann Equation -- 10. Discrete Models of Boltzmann Equation -- 11. Method of Spherical Harmonics and Relaxation of Maxwellian Gas -- 12. Discrete Boltzmann Equation Models for Mixtures -- 13. Quantum Hamiltonians and Kinetic Equations -- 14. Modeling of the Limit Problem for the Magnetically Noninsulated Diode -- 15. Generalized Liouville Equation and Approximate Orthogonal Decomposition Methods; Glossary of Terms and Symbols.
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.
Kinetic theory of gases.
Evolution equations.