The grazing collisions asymptotics of the non cut-off Kac equation

Mathematical Modelling and Numerical Analysis

Volumn 32, Issue 6, 1998, Pages 763-772

  Toscani, G ^a  

^a UNIVERSITY OF PAVIA   (Italy)

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EID: 0032328649     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an/1998320607631     Document Type: Article

References (17)

1. A. A. ARSEN'EV and O. E. BURYAK, "On the connection between a solution of the Boltzmann equation and a solution of the Landau-Fokker-Planck equation". Math. USSR Sbornik, 69 (2), 465-478 (1991).
2. E. A. CARLEN, E. GABETTA, G. TOSCANI, "Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas", to appear on Comm. Math. Phys. (1997).
3. C. CERCIGNANI, The Boltzmann equation and its applications. Springer, New York (1988).
4. P. DEGOND and B. LUCQUIN-DESREUX, "The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case", Math. Mod. Meth. in appl. Sci., 2 (2), 167-182 (1992).
5. L. DESVILLETTES, "On asymptotics of the Boltzmann equation when the collisions become grazing", Transp. theory and stat. phys., 21 (3), 259-276 (1992).
6. L. DESVILLETTES, "About the regularizing properties of the non-cut-off Kac equation", Comm. Math. Phys., 168 (2), 417-440 (1995).
7. E. GABETTA, L. PARESCHI, "About the non cut-off Kac equation: Uniqueness and asymptotic behaviour", Comm. Appl. Nonlinear Anal., 4, 1-20 (1997).
8. E. GABETTA, G. TOSCANI, B. WENNBERG, "Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation", J. Stat. Phys. 81, 901-934 (1995).
9. T. GOUDON, "On the Boltzmann equation and its relations to the Landau-Fokker-Planck equation: influence of grazing collisions". To appear in C. R. Acad. Sci., 1997.
10. M. KAC, Probability and related topics in the physical sciences. New York (1959).
11. P. L. LIONS, "On Boltzmann and Landau equations", Phil. Trans. R. Soc. Lond., A(346), 191-204 (1994).
12. P. L. LIONS, G. TOSCANI, "A sthrenghtened central limit theorem for smooth densities", J. Funct. Anal. 128, 148-167 (1995).
13. J. NASH, "Continuity of solutions of parabolic and elliptic equations", Amer. J. Math. 80, 931-957 (1958).
14. G. TOSCANI, "On regularity and asymptotic behaviour of a spatially homogeneous Maxwell gas". Rend. Circolo Mat. Palermo, Serie II, Suppl. 45, 649-662 (1996).
15. G. TOSCANI, "Sur l'inégalité logarithmique de Sobolev", To appear in C. R. Acad. Sci., 1997.
16. C. VlLLANI, "On the Landau equation: weak stability, global existence", Adv. Diff. Eq. 1 (5), 793-818 (1996).
17. C. VILLANI, "On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations".