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

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


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.

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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 with Infinite Components for Multivalued Semiflows. Set-Valued and Variational Analysis, v. 25, n. 1, p. 25-41, MAR 2017. Web of Science Citations: 2.
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. Web of Science Citations: 2.

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