E-viri
PDF
Recenzirano
Odprti dostop
-
Cesbron, L.; Mellet, A.; Puel, M.
Archive for rational mechanics and analysis, 02/2020, Letnik: 235, Številka: 2Journal Article
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 Cesbron (Commun Math Phys 364:233–286, 2018 ) in the case of specular reflection conditions at the boundary and does not seem to have received a lot of attention previously.
