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Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach

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  • We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.
    Mathematics Subject Classification: 76P05, 26A33, 22E46, 53C35, 57S20.

    Citation:

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  • [1]

    C. Bardos, R. Santos and R. Sentis, Diffusion approximation and computation of the critical size, Trans. A. M. S., 284 (1984), 617-649.doi: 10.1090/S0002-9947-1984-0743736-0.

    [2]

    N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys., 37 (1996), 3306-3333.doi: 10.1063/1.531567.

    [3]

    N. Ben Abdallah, A. Mellet and M. PuelAnomalous diffusion limit for kinetic equations with degenerate collision frequency, Math. Models Methods Appl. Sci., to appear.

    [4]

    A. Bensoussan, J.-L. Lions and G. Papanicolaou, Boundary layers and homogenization of transport processes, Publ. Res. Inst. Math. Sci., 15 (1979), 53-157.doi: 10.2977/prims/1195188427.

    [5]

    A. V. Bobylev, J. A. Carrillo and I. M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Statist. Phys., 98 (2000), 743-773.doi: 10.1023/A:1018627625800.

    [6]

    A. V. Bobylev and I. M. Gamba, Boltzmann equations for mixtures of Maxwell gases: Exact solutions and power like tails, J. Stat. Phys., 124 (2006), 497-516.doi: 10.1007/s10955-006-9044-8.

    [7]

    P. Degond, T. Goudon and F. Poupaud, Diffusion limit for nonhomogeneous and non-micro-reversibles processes, Indiana Univ. Math. J., 49 (2000), 1175-1198.

    [8]

    M. H. Ernst and R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, J. Statist. Phys., 109 (2002), 407-432.doi: 10.1023/A:1020437925931.

    [9]

    T. Goudon and A. Mellet, On fluid limit for the semiconductors Boltzmann equation, Journal Diff. Equations, 189 (2003), 17-45.doi: 10.1016/S0022-0396(02)00096-7.

    [10]

    E. W. Larsen and J. B. Keller, Asymptotic solution of neutron transport problems for small mean free paths, J. Math. Phys., 15 (1974), 75-81.doi: 10.1063/1.1666510.

    [11]

    N. Masmoudi and M.-L. Tayeb, On the diffusion limit of a semiconductor Boltzmann-Poisson system without micro-reversible process, Comm. Partial Differential Equations, 35 (2010), 1163-1175.

    [12]

    A. Mellet, Diffusion limit of a nonlinear kinetic model without the detailed balance principle, Monatshefte f. Mathematik, 134 (2002), 305-329.doi: 10.1007/s605-002-8265-1.

    [13]

    A. Mellet, Fractional diffusion limit for collisional kinetic equations: A moments method, Indiana Univ. Math. J., 59 (2010), 1333-1360.doi: 10.1512/iumj.2010.59.4128.

    [14]

    A. Mellet, S. Mischler and C. Mouhot, Fractional diffusion limit for collisional kinetic equations, Arch. Ration. Mech. Anal., 199 (2011), 493-525.doi: 10.1007/s00205-010-0354-2.

    [15]

    D. A. Mendis and M. Rosenberg, Cosmic dusty plasma, Annu. Rev. Astron. Astrophys., 32 (1994), 419-463.doi: 10.1146/annurev.aa.32.090194.002223.

    [16]

    A. Pulvirenti and G. Toscani, Asymptotic properties of the inelastic Kac model, J. Statist. Phys., 114 (2004), 1453-1480.doi: 10.1023/B:JOSS.0000013964.98706.00.

    [17]

    D. Summers and R. M. Thorne, The modified plasma dispersion function, Phys. Fluids, 83 (1991), 1835-1847.

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