Continuity of global attractors: The use of correctors to obtain better rate of convergence.

• Grant number: 12/00033-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2012
• End date: November 20, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Cesar Augusto Esteves das Neves Cardoso
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The continuity of the asymptotic dynamics under perturbation is of vital importance to the investigation of real world phenomena through mathematical modelling. In the modelling are used measurements, observations, empiric laws, less important factors are neglected, etc. In all these processes, errors are unavoidably present and the model obtained is an approximation (fair) of the ideal model. In this way, the result of such studies will only have any meaning if they are robust under perturbations (of all kind) in the model. In this project our aim is to study the continuity of the asymptotic dynamics with respect to perturbations and, in particular, exploit the possibility of improvement in the rate of convergence of global attractors by introducing correctors, inspired by the results in homogenization theory and in the works [1] and [2].

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)

BORTOLAN, M. C.; CARDOSO, C. A. E. N.; CARVALHO, A. N.; PIRES, L.. Lipschitz perturbations of Morse-Smale semigroups. Journal of Differential Equations, v. 269, n. 3, p. 1904-1943, JUL 15 2020. (12/00033-3, 18/10997-6)

Academic Publications

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

CARDOSO, Cesar Augusto Esteves das Neves. Continuity of global attractors: the use of correctors to obtain better convergence rates. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.