The Boltzmann Equation and Its Applications
Statistical mechanics may be naturally divided into two branches, one dealing with equilibrium systems, the other with nonequilibrium systems. The equilibrium properties of macroscopic systems are defined in principle by suitable averages in well-defined
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F. John 1. E. Marsden
L. Sirovich
Advisors
M. Ghil J. K. Hale 1. Keller K. Kirchgassner B. Matkowsky J. T. Stuart A. Weinstein
Applied Mathematical Sciences I. John: Partial Differential Equations, 4th ed.
2. 3. 4. 5. 6.
Sirovich: Techniques of Asymptotic Analysis. Hale: Theory of Functional Differential Equations, 2nd ed. Percus: Combinatorial Methods. von Mises/Friedrichs: Fluid Dynamics. Freiberger/Grenander: A Short Course in Computational Probability and Statistics. 7. Pipkin: Lectures on Viscoelasticity Theory. 9. Friedrichs: Spectral Theory of Operators in Hilbert Space. II. Wolovich: Linear Multivariable Systems. 12. Berkovitz: Optimal Control Theory. 13. BlumaniCole: Similarity Methods for Differential Equations. 14. Yoshizawa: Stability Theory and the Existence of Periodic Solution and Almost Periodic Solutions. 15 .. Braun: Differential Equations and Their Applications, 3rd ed. 16. Lefschetz: Applications of Algebraic Topology. 17. CollatzlWetterIing: Optimization Problems. 18. Grenander: Pattern Synthesis: Lectures in Pattern Theory, Vol I. 20. Driver: Ordinary and Delay Differential Equations. 21. Courant/Friedrichs: Supersonic Flow and Shock Waves. 22. Rouche/Habets/Laloy: Stability Theory by Liapunov's Direct Method. 23. Lamperti: Stochastic Processes: A Survey of the Mathematical Theory. 24. Grenander: Pattern Analysis: Lectures in Pattern Theory, Vol. II. 25. Davies: Integral Transforms and Their Applications, 2nd ed. 26. Kushner/Clark: Stochastic Approximation Methods for Constrained and Unconstrained Systems 27. de Boor: A Practical Guide to Splines. 28. Keilson: Markov Chain Models-Rarity and Exponentiality. 29. de Veubeke: A Course in Elasticity. 30. Sniatycki: Geometric Quantization and Quantum Mechanics. 31. Reid: Sturmian Theory for Ordinary Differential Equations. 32. Meis/Markowitz: Numerical Solution of Partial DilTerential Equations. 33. Grenander: Regular Structures: Lectures in Pattern Theory, Vol. III. 34. Kevorkian/Cole: Perturbation Methods in Applied Mathematics. 35. Carr: Applications of Centre Manifold Theory. 36. Bengtsson/GhiJ/Kallen: Dynamic Meterology: Data Assimilation Methods. 37. Saperstone: Semidynamical Systems in Infinite Dimensional Spaces. 38. Lichtenberg/Lieberman: Regular and Stochastic Motion. 39. Piccini/StampacchiaiVidossich: Ordinary Differential Equations in RO. 40. NayJor/Sell: Linear Operator Theory in Engineering and Science: 41. Sparrow: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. 42. Guckenheimer/Holmes: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. 43. Ockendon/Tayler: Inviscid Fluid Flows. (continued following index)
Carlo Cercignani
The Boltzmann Equation and Its Applications With 42 Illustrations
Springer Science+Business Media, LLC
Carlo Cercignani Department of Mathematics Politecnico di Milano 20133 Milano (1) Italy
Editors F. John Courant Institute of Mathematical Sciences New York University New York, NY 10012 U.S.A.
J. E. Marsden Department of Mathematics University of Californi
