Derivation of the Boltzmann equation from particle dynamics
Kōhei Uchiyama
Source: Hiroshima Math. J. Volume 18, Number 2
(1988), 245-297.
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Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206129724
Mathematical Reviews number (MathSciNet): MR955371
Zentralblatt MATH identifier: 0656.60110
References
[1] Aizenman, M., A sufficient condition for the avoidance of sets by measure preserving flows in R", Duke Math. J. 45 (1978), 809-814.
Zentralblatt MATH: 0471.28015
Mathematical Reviews (MathSciNet): MR518107
[2] Alexander, K., The infinite hard sphere system, Ph. D. Thesis, Dept. Math. Univ. of California at Berkeley (1975).
[3] Billingsley, P., Convergence of Probability Measures, Wiley, New York (1968).
Zentralblatt MATH: 0172.21201
Mathematical Reviews (MathSciNet): MR233396
[4] Cercignani, C, On the Boltzmann Equation for Rigid Spheres, Transport Th. and Stat. Phys. 2(1972), 211-225.
Zentralblatt MATH: 0295.76048
Mathematical Reviews (MathSciNet): MR449375
[5] Grad, H., Principles of the kinetic theory of gases, Handbuch der Physik 12, Flgge, ed., Springer, Berlin, (1958), 205-294.
Mathematical Reviews (MathSciNet): MR135535
[6] Illner, R., and Pulvirenti, M., Gloval validity of the Boltzmann equation for a twodimensional rare gas in vacuum, Commun. Math. Phys. 105 (1986), 189-203.
Zentralblatt MATH: 0609.76083
Mathematical Reviews (MathSciNet): MR849204
[7] Kac, M., Foundation of kinetic theory, Proceedings of 3rd Berkeley Symposium on Math. Stat. and Prob., Vol. 3, (1956), 171-197.
Zentralblatt MATH: 0072.42802
Mathematical Reviews (MathSciNet): MR84985
[8] King, F., BBGKY hierarchy for positive potentials, Ph. D. Thesis, Dep. of Math., Univ. of California at Berkeley (1975).
[9] Lanford III, O. E., Time evolution of large classical systems, in "Dynamical Systems and Applications", Lecture Notes in Phys. 38 (1975), 1-111.
Zentralblatt MATH: 0329.70011
Mathematical Reviews (MathSciNet): MR479206
[10] Lanford III, O. E., On a derivation of the Boltzmann equation, in "international Conference on Dynamical Systems in Mathematical Physics", Soc. Math. France, Asterisque 40 (1976), 117-137.
Zentralblatt MATH: 0353.70020
Mathematical Reviews (MathSciNet): MR459449
[11] Lebowitz, J. L. and Spohn, H., On the time evolution of macroscopic systems, Comm. Pure and Appl. Math. 36 (1983), 595-613.
Zentralblatt MATH: 0537.76057
Mathematical Reviews (MathSciNet): MR716198
[12] McKean, H. P., Propagation of chaos for a class of non-linear parabolic equations, Lecture Series in Differential Equations 7, Catholic Univ. (1967), 41-57.
Zentralblatt MATH: 0181.44401
Mathematical Reviews (MathSciNet): MR233437
[13] Takahashi, Y., On a class of Bogoliubov equations and the time evolution in classical statistical mechanics, in "Random field", Vol. II, J. Fritz, J. L. Lebowitz and D. J. Szasz, ed., North-Holland Amsterdam-Oxford-New York (1979), 1033-1056.
Zentralblatt MATH: 0495.28017
Mathematical Reviews (MathSciNet): MR712726
[14] Spohn, H., Kinetic equations from Hamiltonian dynamics: Markov limits, Reviews of Modern Physics 53 (1980), 569-615.
Zentralblatt MATH: 0399.60082
Mathematical Reviews (MathSciNet): MR578142
[15] Spohn, H., On the integrated form of the BBGKY hierarchy for hard spheres, preprint
[16] Uchiyama, K., On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation, J. Stat. Phys. 52 (1988).
Zentralblatt MATH: 1083.82532
Mathematical Reviews (MathSciNet): MR968589
Hiroshima Mathematical Journal