Fractional diffusion limit of a linear kinetic equation in a bounded domain

2016/07/04 by Aceves-Sanchez, Pedro, Schmeiser, Christian
#26A33 #35B40 #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.00855

Abstract

A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs from standard formulations. It can be interpreted as the forward Kolmogorow equation of a stochastic process with jumps along straight lines, remaining inside the domain.

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