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On the Kac model for the Landau equation
1. | Laboratoire de Mathématiques, Université Paris-Sud 11, bât. 425, 91405 Orsay, France |
2. | Dipartimento di Matematica Guido Castelnuovo, Università La Sapienza - Roma, P.le A. Moro, 5 00185 Roma, Italy, Italy |
References:
[1] |
A. A. Arsen'ev and O. E. Buryak, On a connection between the solution of the Boltzmann equation and the solution of the Landau-Fokker-Planck equation, (Russian), Mat. Sb., 181 (1992), 435-446; translation in Math. USSR-Sb., 69 (1991), 465-478. |
[2] |
R. Balescu, "Equilibrium and Nonequilibrium Statistical Mechanics,'' John Wiley & Sons, New-York, 1975. |
[3] |
L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. II. $H$-theorem and applications, Comm. Partial Differential Equations, 25 (2000), 261-298.
doi: 10.1080/03605300008821513. |
[4] |
L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness, Comm. Partial Differential Equations, 25 (2000), 179-259.
doi: 10.1080/03605300008821512. |
[5] |
T. Goudon, On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions, J. Stat. Phys., 89 (1997), 751-776.
doi: 10.1007/BF02765543. |
[6] |
M. Kac, Foundations of kinetic theory, in "Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability," University of California Press, Berkeley and Los Angeles (1956). |
[7] |
A. I. Khinchin, "Mathematical Foundations of Information Theory," New York: Dover, 1957. |
[8] |
L. P. Pitaevskii and E. M. Lifshitz, "Course of Theoretical Physics. Vol. 10," Pergamon Press, Oxford-Elmsford, N.Y. 1981. |
[9] |
R. Peyre, Some ideas about quantitative convergence of collision models to their mean field limit, J. Stat. Phys., 136 (2009), 1105-1130.
doi: 10.1007/s10955-009-9820-3. |
[10] |
M. Pulvirenti, The weak-coupling limit of large classical and quantum systems, in "International Congress of Mathematicians," Eur. Math. Soc., Zürich (2006). |
[11] |
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal., 143 (1998), 273-307.
doi: 10.1007/s002050050106. |
show all references
References:
[1] |
A. A. Arsen'ev and O. E. Buryak, On a connection between the solution of the Boltzmann equation and the solution of the Landau-Fokker-Planck equation, (Russian), Mat. Sb., 181 (1992), 435-446; translation in Math. USSR-Sb., 69 (1991), 465-478. |
[2] |
R. Balescu, "Equilibrium and Nonequilibrium Statistical Mechanics,'' John Wiley & Sons, New-York, 1975. |
[3] |
L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. II. $H$-theorem and applications, Comm. Partial Differential Equations, 25 (2000), 261-298.
doi: 10.1080/03605300008821513. |
[4] |
L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness, Comm. Partial Differential Equations, 25 (2000), 179-259.
doi: 10.1080/03605300008821512. |
[5] |
T. Goudon, On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions, J. Stat. Phys., 89 (1997), 751-776.
doi: 10.1007/BF02765543. |
[6] |
M. Kac, Foundations of kinetic theory, in "Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability," University of California Press, Berkeley and Los Angeles (1956). |
[7] |
A. I. Khinchin, "Mathematical Foundations of Information Theory," New York: Dover, 1957. |
[8] |
L. P. Pitaevskii and E. M. Lifshitz, "Course of Theoretical Physics. Vol. 10," Pergamon Press, Oxford-Elmsford, N.Y. 1981. |
[9] |
R. Peyre, Some ideas about quantitative convergence of collision models to their mean field limit, J. Stat. Phys., 136 (2009), 1105-1130.
doi: 10.1007/s10955-009-9820-3. |
[10] |
M. Pulvirenti, The weak-coupling limit of large classical and quantum systems, in "International Congress of Mathematicians," Eur. Math. Soc., Zürich (2006). |
[11] |
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal., 143 (1998), 273-307.
doi: 10.1007/s002050050106. |
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