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Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations

Abstract:

We consider a nonlocal aggregation equation with degenerate diffusion, which describes the mean‐field limit of interacting particles driven by nonlocal interactions and localized repulsion. When the interaction potential is attractive, it is previously known that all steady states must be radially decreasing up to a translation, but uniqueness (for a given mass) within the radial class was open, except for some special interaction potentials. For general attractive potentials, we show that th...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1002/cpa.21950

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-6897-1060
Publisher:
Wiley
Journal:
Communications on Pure and Applied Mathematics More from this journal
Volume:
75
Issue:
1
Pages:
3-59
Publication date:
2020-10-06
Acceptance date:
2020-06-25
DOI:
EISSN:
1097-0312
ISSN:
0010-3640
Language:
English
Keywords:
Pubs id:
1131619
Local pid:
pubs:1131619
Deposit date:
2020-09-11

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