Author
Carrillo de la Plata, J
Hittmeir, S
Volzone, B
Yao, Y
Journal title
Inventiones Mathematicae
DOI
10.1007/s00222-019-00898-x
Issue
3
Volume
218
Last updated
2022-08-05T04:54:13.11+01:00
Page
889-977
Abstract
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the particular case of Newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation-diffusion equations towards this unique equilibrium profile up to translations as ๐‘กโ†’โˆž.
Symplectic ID
1098219
Favourite
On
Publication type
Journal Article
Publication date
25 Jul 2019
Please contact us for feedback and comments about this page. Created on 02 Apr 2020 - 13:05.