Continuity of attractors for dynamical systems: Morse decompositions, equiattraction and unbounded domains

Author(s)

Henrique Barbosa da Costa

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2016-07-28

Examining board members

Alexandre Nolasco de Carvalho; Ma To Fu; Tomás Caraballo Garrido; Antonio Luiz Pereira; Jacson Simsen

• Advisor: Alexandre Nolasco de Carvalho

Abstract

In this work we study assimptotic properties of parabolic problems under some different view of points, particularlly interested in the stability properties of the systems. We study equi-attraction in the non autonomous case using skew-product semiflows, which transform the non autonomous dynamical system into a autonomous one in a convenient phase space. For multivalued semiflows, in which the semiflow is a set valued function, we develop the Morse decomposition and show its equivalence with admiting a Lyapunov funcional, wich is a important result on the semigroup theory. We also study the continuity of the asymptotic dynamic for a parabolic problem in an unbouded domain when we approach it by bounded ones. (AU)

• FAPESP's process: 11/21456-7 - Continuity of attractors for dynamical systems: Unbounded domains and uniformly-local spaces.
• Grantee: Henrique Barbosa da Costa
• Support Opportunities: Scholarships in Brazil - Doctorate