Concentration phenomena arising in Aggregation Fast-Diffusion equations

par Alejandro Fernandez Jimenez (U. Oxford)

mercredi 16 oct. 2024, 10:00 → 11:30 Europe/Paris

On this talk we will discuss about asymptotic behaviour of the family of
Aggregation-Diffusion Equations
∂_tρ = ∆ρ^m + div(ρ∇(V + W ∗ ρ)),

for 0 < m < 1. We rely on compactness arguments, and the gradient flow
structure of the problem to obtain convergence of the solutions when t → ∞.
Then, we pass to the mass equation and we use viscosity solutions to characterise
the limit and discuss the existence of Dirac deltas.

The talk presents joint work with Prof. J.A. Carrillo and Prof. D. G ́omez-
Castro.