SMS scnews item created by Sanjana Bhardwaj at Wed 12 Jul 2023 1604
Type: Seminar
Modified: Wed 12 Jul 2023 1616
Distribution: World
Expiry: 18 Jul 2023
Calendar1: 17 Jul 2023 1100-1200
CalLoc1: AGR Carslaw 829
CalTitle1: Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications
Auth: sanjana@wh8hb0j3.staff.wireless.sydney.edu.au (sbha9594) in SMS-SAML

AGR Seminar

Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications

Jose Carrillo

Dear friends and colleagues,   
on Monday, 17 July 2023 at
    11 AM for Sydney

Professor@ Oxford University, UK; Jose Carrillon is giving a talk on 

Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications

Abstract:

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 to 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 ow structure of these problems. The theoretical analysis of the asymptotic stability of the different branches of solutions is a challenging open problem.
You can also use the zoom link to join: https://uni-sydney.zoom.us/j/84818062069?pwd=cjlrSTRiT3MvYmE5WmlNNGJKdERHQT09 Password: 690172
Everyone is welcome to join for lunch after the seminar.

Sanjana
On behalf of Daniel H.