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Uniqueness of stationary states for singular Keller–Segel type models

Abstract:

We consider a generalised Keller–Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are more singular than Newtonian interaction. We show uniqueness of stationary states (if they exist) in any dimension both in the diffusion-dominated regime and in the fair-competition regime when attraction and repulsion are in balance. As stationary states are radially symmetric decreasing, the question of uniqueness reduces t...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.na.2020.112222

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8819-4660
Publisher:
Elsevier
Journal:
Nonlinear Analysis More from this journal
Volume:
205
Issue:
April 2021
Article number:
112222
Publication date:
2020-12-13
Acceptance date:
2020-12-02
DOI:
ISSN:
0362-546X
Language:
English
Keywords:
Pubs id:
1098411
Local pid:
pubs:1098411
Deposit date:
2021-02-04

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