Fractional diffusion limit for collisional kinetic equations: A moments method

2009/10/08 by Antoine Mellet, Mellet, Antoine · 1 citation
Mathematics · #26A33 #35B40 #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0910.1570

openalex publication_date 2009/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to hydrodynamic limits of linear kinetic equations when the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a Maxwellian distribution. We show that the long time/small mean free path behavior of the solution of the kinetic equation is described by a fractional diffusion equation. The method that we introduce is somewhat reminiscent of the so-called "moments method" which plays an important role in kinetic theory.

Citations

• Cosmic Dusty Plasma

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