Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Carrillo:2019,
author = {Carrillo, JA and Gvalani, RS and Pavliotis, GA and Schlichting, A},
publisher = {ArXiv},
title = {Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus},
url = {http://arxiv.org/abs/1806.01719v3},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - We study the McKean-Vlasov equation∂t = β−1 + κ ∇·(∇(W  )) ,with periodic boundary conditions on the torus. We first study the global asymptotic stability of thehomogeneous steady state. We then focus our attention on the stationary system, and prove the existenceof nontrivial solutions branching from the homogeneous steady state, through possibly infinitely manybifurcations, under appropriate assumptions on the interaction potential. We also provide sufficientconditions for the existence of continuous and discontinuous phase transitions. Finally, we showcasethese results by applying them to several examples of interaction potentials such as the noisy Kuramotomodel for synchronisation, the Keller–Segel model for bacterial chemotaxis, and the noisy Hegselmann–Krausse model for opinion dynamics.
AU  - Carrillo,JA
AU  - Gvalani,RS
AU  - Pavliotis,GA
AU  - Schlichting,A
PB  - ArXiv
PY  - 2019///
TI  - Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
UR  - http://arxiv.org/abs/1806.01719v3
UR  - http://hdl.handle.net/10044/1/72137
ER  -
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