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

We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.

[1]  Antoine Mellet,et al.  Fractional Diffusion Limit for Collisional Kinetic Equations , 2008, 0809.2455.

[2]  Antoine Mellet,et al.  Fractional diffusion limit for collisional kinetic equations: A moments method , 2009, 0910.1570.

[3]  G. Toscani,et al.  Asymptotic Properties of the Inelastic Kac Model , 2004 .

[4]  Pierre Degond,et al.  On a hierarchy of macroscopic models for semiconductors , 1996 .

[5]  M. H. Ernst,et al.  Scaling Solutions of Inelastic Boltzmann Equations with Over-Populated High Energy Tails , 2002 .

[6]  Thierry Goudon,et al.  On fluid limit for the semiconductors Boltzmann equation , 2003 .

[7]  Pierre Degond,et al.  Diffusion limit for non homogeneous and non-micro-reversible processes , 2000 .

[8]  Irene M. Gamba,et al.  On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions , 2000 .

[9]  Nader Masmoudi,et al.  Diffusion Limit of a Semiconductor Boltzmann-Poisson System , 2007, SIAM J. Math. Anal..

[10]  A. V. Bobylev,et al.  Boltzmann Equations For Mixtures of Maxwell Gases: Exact Solutions and Power Like Tails , 2006 .

[11]  Diffusion Limit of a Non-Linear Kinetic Model without the Detailed Balance Principle , 2002 .

[12]  A. Bensoussan,et al.  Boundary Layers and Homogenization of Transport Processes , 1979 .

[13]  D. A. Mendis,et al.  COSMIC DUSTY PLASMA , 1994 .

[14]  Antoine Mellet,et al.  ANOMALOUS DIFFUSION LIMIT FOR KINETIC EQUATIONS WITH DEGENERATE COLLISION FREQUENCY , 2011 .

[15]  C. Bardos,et al.  DIFFUSION APPROXIMATION AND COMPUTATION OF THE CRITICAL SIZE , 1984 .

[16]  Richard M. Thorne,et al.  The modified plasma dispersion function , 1991 .

[17]  N. Masmoudi,et al.  On the Diffusion Limit of a Semiconductor Boltzmann–Poisson System Without Micro-Reversible Process , 2010 .

[18]  J. Keller,et al.  Asymptotic solution of neutron transport problems for small mean free paths , 1974 .