Orateur
David Gómez-Castro
Description
The aim of this talk is to discuss a finite-volume scheme for the aggregation-diffusion family of equations with non-linear mobility
∂t ρ = div (m(ρ) D (U'() + V + W*ρ))
in bounded domains with no-flux conditions.
We will present basic properties of the scheme: existence, decay of a free, and comparison principle (where applicable); and a convergence-by-compactness result for the saturation case where m(0)=m(1)= 0, under general assumptions on m, U, V, and W.
The results are joint works published with J.-A. Carrillo and A. Fernandez-Jimenez.
At the end of the talk, we will discuss an extension to the Porous-Medium Equation with non-local pressure that corresponds to m(ρ) = ρ^m, U, V = 0 and W(x) = c|x|^{-d-2s}.