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arXiv · 1805.04903

Fractional Diffusion limit of a kinetic equation with Diffusive boundary conditions in the upper-half space

Ludovic Cesbron·Antoine Mellet·Marjolaine Puel
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Abstract

We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time asymptotic, we derive a fractional diffusion equation with a nonlocal Neumann boundary condition for the density of particles. Interestingly, this asymptotic equation is different from the one derived by L. Cesbron in [7] in the case of specular reflection conditions at the boundary and does not seem to have receive a lot of attention previously.

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Ludovic Cesbron, Antoine Mellet, Marjolaine Puel. 2018-06-27. Fractional Diffusion limit of a kinetic equation with Diffusive boundary conditions in the upper-half space. https://doi.org/10.1007/s00205-019-01442-0

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