Fermi–Dirac–Fokker–Planck equation: Well-posedness & long-time asymptotics

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Carrillo , José A.; Laurençot , Philippe; Rosado , Jesús;
(2009)
  • Publisher: Elsevier BV
  • Journal: Journal of Differential Equations, volume 247, issue 8, pages 2,209-2,234 (issn: 0022-0396)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1016/j.jde.2009.07.018
  • Subject: [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | MSC: 35Q84 (35B35 35B40 82C35) | [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] | Analysis

International audience; 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 fin... View more
  • References (26)
    26 references, page 1 of 3

    [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.

    [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, Applied Mathematics Letters 21 (2008), 148-154.

    [6] P.-H. Chavanis, Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics and two-dimensional turbulence, Phys. Rev. E 68 (2003), 036108.

    [7] P.-H. Chavanis, Generalized thermodynamics and kinetic equations: Boltzmann, Landau, Kramers and Smoluchowski, Phys. A 332 (2004), 89-122.

    [8] P.-H. Chavanis, Generalized Fokker-Planck equations and effective thermodynamics, Phys. A 340 (2004), 57-65.

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

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

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

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