Existence of ground states for aggregation-diffusion equations
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Accepted version
Author(s)
Carrillo de la Plata, JA
Delgadino, M
Patacchini, F
Type
Journal Article
Abstract
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not.
Date Issued
2018-10-16
Online Publication Date
2018-10-16
2018-11-28T14:48:18Z
Date Acceptance
2018-09-06
ISSN
1793-6861
Publisher
World Scientific Publishing
Journal / Book Title
Analysis and Applications
Copyright Statement
© The Author(s). This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
Source Database
manual-entry
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P031587/1
Subjects
0102 Applied Mathematics
General Mathematics
Publication Status
Published online
Date Publish Online
2018-10-16