Published Paper

Inserted: 29 jul 2024

Journal: J. Funct. Anal.
Volume: 287
Number: 2
Year: 2024
Doi: 10.1016/j.jfa.2024.110465

Abstract:

We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s. The addition of a quadratic diffusion term produces a more precise competition with the aggregation term for small s, as they have the same scaling if s=0. We prove existence and uniqueness of stationary states and we characterize their asymptotic behavior as s goes to zero. Moreover, we prove existence of gradient flow solutions to the evolution problem by applying the JKO scheme.