Fractional Diffusion Limits of Non-Classical Transport Equations

2016/07/14 by Martin Frank, Frank, Martin, Weiran Sun +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #35Q20 #35Q70 #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #FOS: Mathematics #Nuclear reactor physics and engineering #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1607.04028

openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics & computation and supercomputing in nuclear applications, 2007]. By introducing appropriate scaling parameters, the limits will be either regular or fractional diffusion equations depending on the tail behaviour of the path-length distribution. Our analysis uses the Fourier transform combined with a moment method. We conclude with remarks on the diffusion limit of the periodic Lorentz gas equation.

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