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Long time behaviour and phase transitions for the McKean-Vlasov equation

Date: Tuesday, March 13, 2018 14:00 - 15:00
Speaker: Grigorios Pavliotis (Imperial College London)
Location: Mondi Seminar Room 2, Central Building
Series: Formal Sciences Seminar
Host: Jan Maas


We study the long time behaviour and the number and structure of stationary solutions for the McKean-Vlasov equation, a nonlinear nonlocal Fokker-Planck type equation that describes the mean field limit of a system of weakly interacting diffusions. We consider two cases: the McKean-Vlasov equation in a multiscale confining potential with quadratic, Curie-Weiss, interaction (the so-called Dasai-Zwanzig model), and the McKean-Vlasov dynamics on the torus with periodic boundary conditions and with a localized interaction. Our main objectives are the study of convergence to a stationary state and the construction of the bifurcation diagram for the stationary problem. The application of our work to the study of models for opinion formation is also discussed.
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