30 nov 2015 -- 15:00
Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma
Abstract.
We construct solutions with finite and infinite type-II blow-up (and analyze their stability) in two related parabolic problems: the standard semilinear heat equation with a power nonlinearity at the critical exponent in a bounded domain in $\mathbb{R}^N$, and the harmonic map flow from a two-dimensional domain into the sphere $\mathbb{S}^2$. Both problems have stationary states with energy scaling-invariance in entire space which are the building blocks of the bubbling patterns.