Pullback attractor for non-linear parabolic equations with subdifferential principal part

• Grant number: 21/01931-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2021
• End date: September 25, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Heraclio Ledgar López Lázaro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 22/13001-4 - Finite fractal dimension for non-linear parabolic equations with subdifferential principal part, BE.EP.PD

Abstract

This research project deals with the study of the asymptotic behavior of solutions for a class of non-linear parabolic equations with subdifferential principal part and non-Lipschitz perturbations. In particular, it will be of interest to apply these results to a class of incompressible non-Newtonian fluids. (AU)

Scientific publications

(7)

(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; CARVALHO, ALEXANDRE N.; LOPEZ-LAZARO, HERACLIO. Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids. Journal of Mathematical Physics, v. 64, n. 11, p. 29-pg., 2023-11-01. (21/01931-4, 22/13001-4, 20/14075-6)

LOPEZ-LAZARO, HERACLIO; NASCIMENTO, MARCELO J. D.; TAKAESSU JR, CARLOS R.; AZEVEDO, VINICIUS T.. Pullback attractors with finite fractal dimension for a semilinear transfer equation with delay in some non-cylindrical domain. Journal of Differential Equations, v. 393, p. 44-pg., 2024-02-20. (22/13001-4, 22/16305-4, 20/14353-6, 21/01931-4, 20/14075-6, 22/02172-2)

NEYRA, JACKELINE HUACCHA; LOPEZ-LAZARO, HERACLIO; RUBIO, OBIDIO; TAKAESSU JUNIOR, CARLOS R.. Pullback exponential attractor of dynamical systems associated with non-cylindrical problems. Journal of Mathematical Analysis and Applications, v. 547, n. 2, p. 30-pg., 2025-07-15. (21/01931-4, 20/14353-6, 22/13001-4, 22/02172-2)

BEZERRA, FLANK D. M.; LOPEZ-LAZARO, HERACLIO; TAKAESSU, CARLOS R.. Spectral and Probabilistic Analysis of Third-Order Linear Abstract Differential Equations. Journal of Dynamics and Differential Equations, v. N/A, p. 22-pg., 2025-03-17. (22/02172-2, 21/01931-4, 22/13001-4, 20/14353-6)

LOPEZ-LAZARO, HERACLIO; NASCIMENTO, MARCELO J. D.; RUBIO, OBIDIO. Finite fractal dimension of pullback attractors for semilinear heat equation with delay in some domain with moving boundary. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 225, p. 35-pg., 2022-08-15. (19/26841-8, 21/01931-4)

LOPEZ-LAZARO, HEREDITARY HERACLIO LEDGAR; MARIN-RUBIO, PEDRO; PLANAS, GABRIELA. Non-Newtonian incompressible fluids with nonlinear shear tensor and conditions. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 138, p. 20-pg., 2024-07-19. (21/01931-4, 22/13001-4, 19/02512-5)

CUI, HONGYONG; LOPEZ, RODIAK NICOLAI FIGUEROA; LOPEZ-LAZARO, HERACLIO LEDGAR; SIMSEN, JACSON. Multi-valued dynamical systems on time-dependent metric spaces with applications to Navier-Stokes equations. MATHEMATISCHE ANNALEN, v. 390, n. 4, p. 56-pg., 2024-06-14. (21/01931-4, 22/13001-4)