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Seminario doble de EDPs
Contacto 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

ResumenThe classical model for chemotaxis is the planar Keller-Segel system

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


\[\mathbb R^2\times (0,\infty)\]
. 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
, 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. 

Localización Aula 520 del módulo 17