SMRI Seminar: Carrillo -- Nonlocal Aggregation-Diffusion Equations: fast diffusion and partial concentration

SMRI Seminar: 
’Nonlocal Aggregation-Diffusion Equations: fast diffusion and partial concentration’
Jose Carrillo (University of Oxford)

Thursday 20th July, 1:00-2:00pm (AEST) 
Carslaw 375 & Online
(register/join - https://uni-sydney.zoom.us/j/84589809050)


Abstract: We will discuss several recent results for aggregation-diffusion equations 
related to partial concentration of the density of particles. Nonlinear diffusions with 
homogeneous kernels will be reviewed quickly in the case of degenerate diffusions to 
have a full picture of the problem. Most of the talk will be devoted to discuss the less 
explored case of fast diffusion with homogeneous kernels with positive powers. We will 
first concentrate in the case of stationary solutions by looking at minimisers of the 
associated free energy showing that the minimiser must consist of a regular smooth 
solution with singularity at the origin plus possibly a partial concentration of the 
mass at the origin. We will give necessary conditions for this partial mass 
concentration to and not to happen. We will then look at the related evolution problem 
and show that for a given confinement potential this concentration happens in infinite 
time under certain conditions. We will briefly discuss the latest developments when we 
introduce the aggregation term. This talk is based on a series of works in collaboration 
with M. Delgadino, J. Dolbeault, A. Fernandez, R. Frank, D. Gomez-Castro, F. Hoffmann, 
M. Lewin, and J. L. Vazquez. 

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Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on
the SMRI Terrace (accessed through A14-04-L4.36) 

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