Analysis, Geometry, and Dynamical Systems Seminar   RSS

16/04/2019, 15:00 — 16:00 — Room P3.10, Mathematics Building
Phillipo Lappicy, ICMC, Universidade de São Paulo e CAMGSD-IST, Universidade de Lisboa

A nonautonomous Chafee-Infante attractor: a connection matrix approach

The goal of this talk is to present the construction of the global attractor for a genuine nonautonomous variant of the Chafee-Infante parabolic equation in one spatial dimension. In particular, the attractor consists of asymptotic profiles (which correspond to the equilibria in the autonomous counterpart) and heteroclinic solutions between those profiles. We prove the existence of heteroclinic connections between periodic and almost periodic asymptotic profiles, yielding the same connection structure as the well-known Chafee-Infante attractor. This work is still an ongoing project with Alexandre N. Carvalho (ICMC - Universidade de São Paulo).