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Seminario doble de EDPs
Contact Fernando Quirós

Seminario doble de EDPs

Julio D. Rossi (U. Buenos Aires)
Convexity and PDEs

Resumen:  We deal with PDEs given in terms of eigenvalues of the Hessian and their relation with concave/convex functions. We will also include a fractional version of the involved ideas. In the second part we will describe notions of convexity for functions defined on a regular tree (a graph in which each node  -- except one -- is connected with a fixed number of successors and one predecessor).
 
 

Manuel del Pino (U. of Bath)

Blow-up by Aggregation in Chemotaxis


Resumen:  The classical model for chemotaxis is the planar Keller-Segel system

\[ u_t = \Delta u - \]
∇
\[\cdot ( u\]
∇
\[v ),\quad v(\cdot, t) = \frac1{2\pi} \log 1{|\cdot |} * u(\cdot ,t) . \]

in

\[\mathbb R^2\times (0,\infty)\]
. Blow-up of finite mass solutions is expected to take place by aggregation, which is a concentration of bubbling type, common to many geometric flows. We build with precise profiles solutions in the critical-mass case
\[8\pi\]
, in which blow-up in infinite time takes place. We establish stability of the phenomenon detected under arbitrary mass-preserving small perturbations and present new constructions in the finite time blow-up scenario. 

Location Aula 520 del módulo 17
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