[Dottorcomp] Segnalazione Seminario Matematico e Fisico di Milano

[Stefano Lisini]

*Da:* Irene Maria Sabadini <irene.sabadini a polimi.it>
*Inviato:* mercoledì 17 novembre 2021 20:37
*Oggetto:* Avviso di seminario



Si avvisa che in data 2/12/2021, alle ore 17:00, On line, nell'ambito delle
iniziative del Seminario Matematico e Fisico di Milano, si svolgerà il
seguente seminario:

Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase
transitions and applications
Carrillo José Antonio, University of Oxford
This talk will be devoted to an overview of recent results understanding
the bifurcation analysis of nonlinear Fokker-Planck equations arising in a
myriad of applications such as consensus formation, optimization, granular
media, swarming behavior, opinion dynamics and financial mathematics to
name a few. We will present several results related to localized
Cucker-Smale orientation dynamics, McKean-Vlasov equations, and nonlinear
diffusion Keller-Segel type models in several settings. We will show the
existence of continuous or discontinuous phase transitions on the torus
under suitable assumptions on the Fourier modes of the interaction
potential. The analysis is based on linear stability in the right
functional space associated to the regularity of the problem at hand. While
in the case of linear diffusion, one can work in the L2 framework,
nonlinear diffusion needs the stronger Linfty topology to proceed with the
analysis based on Crandall-Rabinowitz bifurcation analysis ! applied t o
the variation of the entropy functional. Explicit examples show that the
global bifurcation branches can be very complicated. Stability of the
solutions will be discussed based on numerical simulations with fully
explicit energy decaying finite volume schemes specifically tailored to the
gradient flow structure of these problems. The theoretical analysis of the
asymptotic stability of the different branches of solutions is a
challenging open problem. This overview talk is based on several works in
collaboration with R. Bailo, A. Barbaro, J. A. Canizo, X. Chen, P. Degond,
R. Gvalani, J. Hu, G. Pavliotis, A. Schlichting, Q. Wang, Z. Wang, and L.
Zhang. This research has been funded by EPSRC EP/P031587/1 and ERC Advanced
Grant Nonlocal-CPD 883363.
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