Fractional Diffusion Limits of Non-Classical Transport Equations
Analysis of PDEs
2016-07-15 v1
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.
Cite
@article{arxiv.1607.04028,
title = {Fractional Diffusion Limits of Non-Classical Transport Equations},
author = {Martin Frank and Weiran Sun},
journal= {arXiv preprint arXiv:1607.04028},
year = {2016}
}