Nonlinear aggregation-diffusion equations with Riesz potentials
Analysis of PDEs
2022-05-27 v1
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.
Cite
@article{arxiv.2205.13520,
title = {Nonlinear aggregation-diffusion equations with Riesz potentials},
author = {Yanghong Huang and Edoardo Mainini and Juan Luis Vázquez and Bruno Volzone},
journal= {arXiv preprint arXiv:2205.13520},
year = {2022}
}