By Mónica Musso, Pontifical Catholic University of Chile, Center for Analysis of Partial Differential Equations

We discuss some new results on globally defined in time positive solutions of the semilinear heat equation with critical power nonlinearity and Dirichlet boundary conditions in a bounded domain. For any given number k we can find a solution that, as time grows, blows up exactly at k points of the domain with a bubbling profile that can be precisely computed. This is joint work with Carmen Cortazar and Manuel del Pino.