Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics

Preprint English OPEN
Carrillo, José A.; Laurençot, Philippe; Rosado, Jesús;
  • Subject: 35B40 | 35K15 | 37B25 | Mathematics - Analysis of PDEs

A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the glo... View more
  • References (19)
    19 references, page 1 of 2

    [1] M. Burger, M. di Francesco, Y. Dolak, The Keller-Segel model for chemotaxis with prevention of overcrowding: linear vs. nonlinear diffusion, SIAM J. Math. Anal. 38 (2006), 1288-1315.

    [2] J. A. Carrillo, A. Ju¨ngel, P. Markowich, G. Toscani, A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatsh. Math. 133 (2001), 1-82.

    [3] J. A. Carrillo, R. J. McCann and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Rational Mech. Anal. 179 (2006), 217-263.

    [4] J. A. Carrillo, G. Toscani, Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations, Math. Methods Appl. Sci. 21 (1998), 1269-1286.

    [5] J. A. Carrillo, J. Rosado, F. Salvarani, 1D nonlinear Fokker-Planck equations for fermions and bosons, to appear in Appl. Math. Lett. (2007).

    [6] C. Dellacherie, P. A. Meyer, Probabilit´es et Potentiel, Hermann, Paris, 1975.

    [7] J. Dolbeault, Kinetic models and quantum effects: a modified Boltzmann equation for Fermi-Dirac particles, Arch. Ration. Mech. Anal. 127 (1994), 101-131.

    [8] M. Escobedo, E. Zuazua, Large time behavior for convection-diffusion equations in RN , J. Funct. Anal. 100 (1991), 119-161.

    [9] T. D. Frank, Classical Langevin equations for the free electron gas and blackbody radiation, J. Phys. A 37 (2004), 3561-3567.

    [10] T. D. Frank, Nonlinear Fokker-Planck Equations, Springer Series in Synergetics, Springer, 2005.

  • Metrics
Share - Bookmark