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Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel

Abstract:

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at infinity, then the linear diffusion overcomes its effect, either attractive or repulsive, for large times independently of the initial data, and solutions behave like the fundamental solution of the heat equation with some rate. The potential $W(x) \sim \log |x|$...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00205-022-01838-5

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8360-3250
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis More from this journal
Volume:
247
Article number:
11
Publication date:
2023-01-31
Acceptance date:
2022-12-21
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
Language:
English
Keywords:
Pubs id:
1180064
Local pid:
pubs:1180064
Deposit date:
2022-11-03

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