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

Naoufel Ben Abdallah; Antoine Mellet; Marjolaine Puel

doi:10.3934/krm.2011.4.873

Article Contents

2011, Volume 4, Issue 4: 873-900. Doi: 10.3934/krm.2011.4.873

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

1.
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne 31062 Toulouse Cedex 9
2.
Department of Mathematics, University of Maryland, College Park, MD 20742
3.
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9

Received: June 30, 2010

Published: November 2011

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Abstract

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

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Mathematics Subject Classification: 76P05, 26A33, 22E46, 53C35, 57S20.

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