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Teaching

Non-compact global attractors for slowly non-dissipative equations By Dr. Juliana Pimentel (Universidade de Lisboa)

  • Class schedule:  Monday, Jun 2nd, 2014 from 2:00 pm to 03:00 pm
  • Location: Building 1, Room 2202
  • Refreshments:  Available @ 13:45 pm 
  • Seminar material available at: link


Abstract

We consider non-dissipative dynamical systems generated by scalar reaction-di ffusion equations. In particular, we address the recently introduced class known as slowly non-dissipative systems, which comprises those systems exhibiting blow-up only in in finite time. By extending known results, we are able to obtain a complete decomposition of the non-compact global attractor. The existence of unbounded trajectories on the attractor requires the introduction of some objects interpreted as equilibria at infinity, yielding a more complex orbit structure than that appearing on dissipative systems. Under this setting, we still manage to determine the heteroclinic connections based on the Sturm permutation method.


Biography

Juliana F. S. Pimentel received her M.Sc. in Applied Mathematics from Universidade de São Paulo in 2010 and her PhD in Mathematics from Instituto Superior Técnico, Universidade de Lisboa in 2014. Her research interests are in Partial Differential Equations and Infinite Dimensional Dinamical Systems. Dr. Pimentel is currently working on the asymptotic behavior of a class of non-dissipative equations