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Long-time behaviour and phase transitions for the Mckean–Vlasov equation on the torus

Abstract:

We study the McKean–Vlasov equation ∂tϱ=β-1Δϱ+κ∇·(ϱ∇(W⋆ϱ)),with periodic boundary conditions on the torus. We first study the global asymptotic stability of the homogeneous steady state. We then focus our attention on the stationary system, and prove the existence of nontrivial solutions branching from the homogeneous steady state, through possibly infinitely many bifurcations, under appropriate assumptions on the interaction potential. We also provide sufficient conditions for the existence ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis More from this journal
Volume:
235
Issue:
1
Pages:
635-690
Publication date:
2019-07-26
Acceptance date:
2019-07-09
DOI:
EISSN:
1432-0673
ISSN:
0003-9527
Language:
English
Keywords:
Pubs id:
1098164
Local pid:
pubs:1098164
Deposit date:
2020-04-07

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