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arXiv · 1510.04918

Fractional-diffusion-advection limit of a kinetic model

Pedro Aceves-Sanchez·Christian Schmeiser
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Abstract

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis is based on bounds derived by relative entropy inequalities and on two recently developed approaches for the macroscopic limit: a Fourier-Laplace transform method for spatially homogeneous data and the so called moment method, based on a modified test function.

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Pedro Aceves-Sanchez, Christian Schmeiser. 2015-10-16. Fractional-diffusion-advection limit of a kinetic model. https://arxiv.org/abs/1510.04918

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