@article{M2AN_1998__32_6_763_0, author = {Toscani, G.}, title = {The grazing collisions asymptotics of the non cut-off {Kac} equation}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {763--772}, publisher = {Elsevier}, volume = {32}, number = {6}, year = {1998}, mrnumber = {1652617}, zbl = {0912.76081}, language = {en}, url = {http://www.numdam.org/item/M2AN_1998__32_6_763_0/} }
TY - JOUR AU - Toscani, G. TI - The grazing collisions asymptotics of the non cut-off Kac equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1998 SP - 763 EP - 772 VL - 32 IS - 6 PB - Elsevier UR - http://www.numdam.org/item/M2AN_1998__32_6_763_0/ LA - en ID - M2AN_1998__32_6_763_0 ER -
Toscani, G. The grazing collisions asymptotics of the non cut-off Kac equation. ESAIM: Modélisation mathématique et analyse numérique, Volume 32 (1998) no. 6, pp. 763-772. http://www.numdam.org/item/M2AN_1998__32_6_763_0/
[1] 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). | MR | Zbl
and , "[2] Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas", to appear on Comm. Math. Phys. (1997). | MR | Zbl
, , , "[3] The Boltzmann equation and its applications. Springer, New York (1988). | MR | Zbl
,[4] The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case", Math. Mod. Meth. in appl. Sci., 2 (2), 167-182 (1992). | MR | Zbl
and , "[5] On asymptotics of the Boltzmann equation when the collisions become grazing", Transp. theory and stat. phys., 21 (3), 259-276 (1992). | MR | Zbl
, "[6] About the regularizing properties of the non-cut-off Kac equation", Comm. Math. Phys., 168 (2), 417-440 (1995). | MR | Zbl
, "[7] About the non cut-off Kac equation: Uniqueness and asymptotic behaviour", Comm. Appl. Nonlinear Anal., 4, 1-20 (1997). | MR | Zbl
, , "[8] Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation", J. Stat. Phys. 81, 901-934 (1995). | MR | Zbl
, , , "[9] 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. | Zbl
, "[10] Probability and related topics in the physical sciences, New York (1959). | MR | Zbl
,[11] On Boltzmann and Landau equations", Phil. Trans. R. Soc. Lond., A(346), 191-204 (1994). | MR | Zbl
, "[12] A sthrenghtened central limit theorem for smooth densities", J. Funct. Anal. 128, 148-167 (1995). | MR | Zbl
, , "[13] Continuity of solutions of parabolic and elliptic equations", Amer. J. Math. 80, 931-957 (1958). | MR | Zbl
, "[14] On regularity and asymptotic behaviour of a spatially homogeneous Maxwell gas". Rend. Circolo Mat. Palermo, Serie II, Suppl. 45, 649-622 (1996). | MR | Zbl
, "[15] Sur l'inégalité logarithmique de Sobolev", To appear in C. R. Acad. Sci., 1997. | MR | Zbl
, "[16] On the Landau equation: weak stability, global existence", Adv. Diff. Eq. 1 (5), 793-818 (1996). | MR | Zbl
, "[17] On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations". | Zbl
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