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Phase transitions for nonlinear nonlocal aggregation-diffusion equations

Abstract:

We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty$. We first prove the existence of possibly infinitely many bifurcations from the spatially homogeneous steady state. We then focus our attention on the associated free energy proving existence of minimisers and even uniqueness for sufficiently weak interactions. In the absence of uniqueness, we show that the ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00220-021-03977-4

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0001-8819-4660
Publisher:
Springer
Journal:
Communications in Mathematical Physics More from this journal
Volume:
382
Issue:
2021
Pages:
485–545
Publication date:
2021-02-14
Acceptance date:
2021-01-15
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Language:
English
Keywords:
Pubs id:
1098401
Local pid:
pubs:1098401
Deposit date:
2021-02-04

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