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*

**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.
Localización Aula 520 del módulo 17