Continuity of attractors for dynamical systems: Unbounded domains and uniformly-local spaces.

• Grant number: 11/21456-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2012
• End date: July 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Henrique Barbosa da Costa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The aim of this work will be to consider the continuity of the asymptotic dynamics for semilinear parabolic and hyperbolic problems under singular perturbations. We will be particularly interested in the cases when the spatial domínio is unbounded. The existence and upper semicontinuity of global attractors for this problems have been considered before whereas the lower semicontinuity has been sistematically neglected. Our aim is to seek ways to consider the lower semicontinuity. Questions related to the non-autônomos case will also be treated.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DA COSTA, HENRIQUE B.; VALERO, JOSE. Morse decompositions and Lyapunov functions for dynamically gradient multivalued semiflows. NONLINEAR DYNAMICS, v. 84, n. 1, SI, p. 19-34, APR 2016. (11/21456-7)

DA COSTA, HENRIQUE B.; VALERO, JOSE. Morse Decompositions with Infinite Components for Multivalued Semiflows. Set-Valued and Variational Analysis, v. 25, n. 1, p. 25-41, MAR 2017. (11/21456-7)

DA COSTA, HENRIQUE B.; VALERO, JOSE. Morse decompositions and Lyapunov functions for dynamically gradient multivalued semiflows. NONLINEAR DYNAMICS, v. 84, n. 1, p. 16-pg., 2016-04-01. (11/21456-7)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

COSTA, Henrique Barbosa da. Continuity of attractors for dynamical systems: Morse decompositions, equiattraction and unbounded domains. 2016. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.