Palestrante: Simão Correia (Universidade de Lisboa)
Data: 03/11/2016 (excepcionalmente, a palestra dessa semana será na 5a feira)
Hora: 13:30 h
Título: Spatial plane waves for the NLS: local existence and stability results
Resumo: In this talk, we shall consider classes of particular solutions for the nonlinear Schrödinger equation. The simplest case appears when one requires that the solution must also satisfy a transport equation in the spatial variables. These solutions are not contained in the known local well-posedness theories. We show local well-posedness on functional spaces which include these solutions and prove their stability with respect to localized perturbations. To this end, we consider a new functional transform, the plane wave transform, which has some quite unexpected properties and generalizes Fourier and Laplace's transform. A comment on further applications to other PDE's shall be made. This is a joint work with Mário Figueira.
Palestrante: Boyan Sirakov (PUC)
Data: 26/10/2016 (quarta feira)
Hora: 15:00 h (horário especial)
Título: Estimativas a priori e regularidade para EDPs elipticas
Resumo: Nesta palestra falaremos de desigualdades de tipo Harnack, fundamentais para a teoria de regularidade, de algumas extensões de fronteira recentes, e de um novo método para mostrar estimativas a priori, para equações elípticas se segunda ordem.
Palestrante: Thierry Barbot (Université d'Avignon)
Título: Flat singular spacetimes, decorated Teichmüller space and singular euclidean surfaces
Resumo: I will present the PhD Thesis work of my student Léo Brunswic, dedicated to flat singular spacetimes. One motivation is to provide a parametrization of singular flat spacetimes of dimension 3, admitting massive particles or even a new type of singularities called extreme BTZ black holes. The parametrization is made through singular euclidean surfaces, that we try to realize as polyhedral surfaces in the spacetime. This approach is connected to the notion of decorated Teichmüller space introduced by R. Penner.