A study about structural stability of atrators for random dynamical systems

• Grant number: 17/21729-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2018
• End date: March 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Alexandre do Nascimento Oliveira Sousa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 18/10633-4 - A study of structural stability for random attractors, BE.EP.DR

Abstract

In this project we study sthocastic evolution equations wich are obtained perturbing a autonomos evolution equations with a noise. We are interested in the assymtopict behavior for these equations and we will search for results that allow a good comparison between the autonomous fixed problem and the stochastic problem obtained by a perturbation. We can associated the solutions of these equations with infinite dimensional random dynamical systems and study continuity and structural stability of random attractors. The aim will be to understand the relation between the global attractor associated with the autonomous problem and the random attractor associated with the perturbed problem, which will be of stochastic nature. (AU)

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)

CARABALLO, TOMAS; LANGA, JOSE A.; CARVALHO, ALEXANDRE N.; OLIVEIRA-SOUSA, ALEXANDRE N.. Continuity and topological structural stability for nonautonomous random attractors. Stochastics and Dynamics, v. 22, n. 07, p. 28-pg., 2022-07-26. (20/14075-6, 17/21729-0, 22/00176-0, 18/10633-4)

CARABALLO, TOMAS; CARVALHO, ALEXANDRE N.; LANGA, JOSE A.; OLIVEIRA-SOUSA, ALEXANDRE N.. The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations. Journal of Mathematical Analysis and Applications, v. 500, n. 2, p. 27-pg., 2021-03-15. (18/10997-6, 18/10633-4, 17/21729-0)

CARABALLO, TOMAS; CARVALHO, ALEXANDRE N.; LANGA, JOSE A.; OLIVEIRA-SOUSA, ALEXANDRE N.. Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations. ASYMPTOTIC ANALYSIS, v. 129, n. 1, p. 27-pg., 2022-01-01. (18/10633-4, 17/21729-0, 18/10997-6)

Academic Publications

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

SOUSA, Alexandre do Nascimento Oliveira. Robustness of nonuniform and random exponential dichotomies with applications to differential equations. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.