Fractional diffusion approximation of kinetic equations in bounded domains.

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Date(s) - 13/11/2018
11 h 00 min - 12 h 00 min


The central question of this talk is: how to confine a non-local diffusion equation, such as the fractional heat equation, to a spatially bounded domain ? The key idea behind the results I will present is to tackle this question from kinetic point of view. Indeed, we can see the fractional heat equation as a diffusion approximation of kinetic models, hence to derive a confined non-local diffusion equation we investigate the fractional diffusion limit of kinetic equations set in spatially bounded domains. We will see, in particular, that the non-local framework is much more sensitive to the kinetic boundary conditions than the classical framework.

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