Derivation of confined non-local diffusion equations
vendredi 9 février 2018, 11h00 - 12h00
The confinement of non-local diffusion processes raises a lot of questions and has received a growing interest in recent years from both the points of view of stochastic analysis and partial differential equations. In this talk I will present an original approach of this problem which consists in considering confined non-local diffusion equations as the anomalous diffusion limits of kinetic equations set on a spatially bounded domain. We will focus mainly on the fractional Vlasov-Fokker-Planck equation in a smooth convex domain with the specular reflection boundary condition and investigate the long time/small mean-free-path asymptotic behaviour of the solution in order to recover, as a limit, a confined version of the fractional heat equation.