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

G. Toscani

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 6, page 763-772
  • ISSN: 0764-583X

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Toscani, G.. "The grazing collisions asymptotics of the non cut-off Kac equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.6 (1998): 763-772. <http://eudml.org/doc/193897>.

@article{Toscani1998,
author = {Toscani, G.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {sufficiently regular initial data; uniform convergence; cross-section; one-dimensional Fokker-Planck equation},
language = {eng},
number = {6},
pages = {763-772},
publisher = {Dunod},
title = {The grazing collisions asymptotics of the non cut-off Kac equation},
url = {http://eudml.org/doc/193897},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Toscani, G.
TI - The grazing collisions asymptotics of the non cut-off Kac equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 6
SP - 763
EP - 772
LA - eng
KW - sufficiently regular initial data; uniform convergence; cross-section; one-dimensional Fokker-Planck equation
UR - http://eudml.org/doc/193897
ER -

References

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  2. [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). Zbl0927.76088MR1669689
  3. [3] C. CERCIGNANI, The Boltzmann equation and its applications. Springer, New York (1988). Zbl0646.76001MR1313028
  4. [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). Zbl0755.35091MR1167768
  5. [5] L. DESVILLETTES, " On asymptotics of the Boltzmann equation when the collisions become grazing", Transp. theory and stat. phys., 21 (3), 259-276 (1992). Zbl0769.76059MR1165528
  6. [6] L. DESVILLETTES, " About the regularizing properties of the non-cut-off Kac equation", Comm. Math. Phys., 168 (2), 417-440 (1995). Zbl0827.76081MR1324404
  7. [7] E. GABETTA, L. PARESCHI, " About the non cut-off Kac equation: Uniqueness and asymptotic behaviour", Comm. Appl. Nonlinear Anal., 4, 1-20 (1997). Zbl0873.45006MR1425012
  8. [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). Zbl1081.82616MR1361302
  9. [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. Zbl0882.76079
  10. [10] M. KAC, Probability and related topics in the physical sciences, New York (1959). Zbl0087.33003MR102849
  11. [11] P. L. LIONS, " On Boltzmann and Landau equations", Phil. Trans. R. Soc. Lond., A(346), 191-204 (1994). Zbl0809.35137MR1278244
  12. [12] P. L. LIONS, G. TOSCANI, " A sthrenghtened central limit theorem for smooth densities", J. Funct. Anal. 128, 148-167 (1995). Zbl0822.60018MR1322646
  13. [13] J. NASH, " Continuity of solutions of parabolic and elliptic equations", Amer. J. Math. 80, 931-957 (1958). Zbl0096.06902MR100158
  14. [14] G. TOSCANI, " On regularity and asymptotic behaviour of a spatially homogeneous Maxwell gas". Rend. Circolo Mat. Palermo, Serie II, Suppl. 45, 649-622 (1996). Zbl0893.76081MR1461111
  15. [15] G. TOSCANI, " Sur l'inégalité logarithmique de Sobolev", To appear in C. R. Acad. Sci., 1997. Zbl0905.46018MR1447044
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  17. [17] C. VILLANI, " On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations". Zbl0912.45011

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