Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability

• Grant number: 18/10997-6
• Support Opportunities: Scholarships abroad - Research
• Start date: September 01, 2018
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Alexandre Nolasco de Carvalho
• Host Investigator: Tomas Caraballo Garrido
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Sevilla (US), Spain

Abstract

The present research project deals with the development of the theory of infinite-dimensional dynamical systems, associated with nonlinear evolution equations, and in particular with the study of the robustness of attractors for autonomous and non-autonomous dynamical systems under perturbations. This research topic is well recognized as an important research theme, even in the restricted context of autonomous dynamic systems (semigroups), and with applications to the development of applied areas such as Engineering and Natural Sciences. From the mathematical point of view, the theme is current and is studied in several well acquainted international research centers. Two centers stand out in the evolution of studies about the robustness of attractors for non-autonomous dynamic systems in the world, the ICMC-USP Non-Linear Dynamic Systems Group (SDNL) and the Stochastic Systems Differential Analysis Group (AESDIF) of the Faculty of Mathematics from the University of Seville.During the visit to the Universidad de Sevilla, the applicant (leader of the SDNL) intends to continue the development of the infinite-dimension dynamical systems theory in collaboration with Professors Tomás Caraballo Garrido (Full Professor - leader of AESDIF) and with outstanding researchers from the group such as Professor José Antonio Langa Rosado (Full Professor at AESDIF).

Scientific publications

(13)

(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)

CARVALHO, ALEXANDRE N.; ROCHA, LUCIANO R. N.; LANGA, JOSE A.; OBAYA, RAFAEL. STRUCTURE OF NON-AUTONOMOUS ATTRACTORS FOR A CLASS OF DIFFUSIVELY COUPLED ODE. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. N/A, p. 23-pg., 2022-05-22. (20/14075-6, 18/10997-6)

CUI, HONGYONG; CARVALHO, ALEXANDRE N.; CUNHA, ARTHUR C.; LANGA, JOSE A.. Smoothing and finite-dimensionality of uniform attractors in Banach spaces. Journal of Differential Equations, v. 285, p. 383-428, JUN 5 2021. (18/10997-6, 18/10634-0, 16/26289-5)

BORTOLAN, M. C.; CARVALHO, A. N.; LANGA, J. A.; RAUGEL, G.. Nonautonomous Perturbations of Morse-Smale Semigroups: Stability of the Phase Diagram. Journal of Dynamics and Differential Equations, OCT 2021. (10/52329-8, 18/10997-6, 12/23724-1)

CARVALHO, ALEXANDRE N.; LANGA, JOSE A.; ROBINSON, JAMES C.. FORWARDS DYNAMICS OF NON-AUTONOMOUS DYNAMICAL SYSTEMS: DRIVING SEMIGROUPS WITHOUT BACKWARDS UNIQUENESS AND STRUCTURE OF THE ATTRACTOR. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 19, n. 4, p. 1997-2013, APR 2020. (18/10997-6)

CARVALHO, ALEXANDRE N.; PIRES, LEONARDO. PARABOLIC EQUATIONS WITH LOCALIZED LARGE DIFFUSION: RATE OF CONVERGENCE OF ATTRACTORS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 53, n. 1, p. 1-23, MAR 2019. (18/10997-6)

BRUSCHI, SIMONE M.; CARVALHO, ALEXANDRE N.; PIMENTEL, JULIANA F.. Limiting Grow-Up Behavior for a One-Parameter Family of Dissipative PDEs. Indiana University Mathematics Journal, v. 69, n. 2, p. 657-683, 2020. (14/03685-7, 18/10997-6)

CARVALHO, ALEXANDRE N.; MOREIRA, ESTEFANI M.. Stability and hyperbolicity of equilibria for a scalar nonlocal one-dimensional quasilinear parabolic problem. Journal of Differential Equations, v. 300, p. 312-336, NOV 5 2021. (20/00104-4, 18/00065-9, 18/10997-6)

CABALLERO, RUBKN; CARVALHO, ALEXANDRE N.; MARIN-RUBIO, PEDRO; VALERO, JOSE. ROBUSTNESS OF DYNAMICALLY GRADIENT MULTIVALUED DYNAMICAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 24, n. 3, SI, p. 1049-1077, MAR 2019. (18/10997-6)

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)

LI, YANAN; CARVALHO, ALEXANDRE N.; LUNA, TITO L. M.; MOREIRA, ESTEFANI M.. A NON-AUTONOMOUS BIFURCATION PROBLEM FOR A NON-LOCAL SCALAR ONE-DIMENSIONAL PARABOLIC EQUATION. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 19, n. 11, p. 5181-5196, NOV 2020. (19/20341-3, 18/10997-6, 18/00065-9)

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)

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)

CABALLERO, RUBKN; CARVALHO, ALEXANDRE N.; MARIN-RUBIO, PEDRO; VALERO, JOSE. ROBUSTNESS OF DYNAMICALLY GRADIENT MULTIVALUED DYNAMICAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 24, n. 3, p. 29-pg., 2019-03-01. (18/10997-6)