Long-time dynamics of semilinear problems

• Grant number: 22/16305-4
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2023
• End date: May 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo José Dias Nascimento
• Grantee: Marcelo José Dias Nascimento
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Flank David Morais Bezerra ; Karina Schiabel ; Vera Lucia Carbone
• Associated research grant(s): 24/02048-5 - Uniform attractors for a family of nonautonomous semilinear evolution equation of second order, AP.R

Abstract

The main objective of this project is to study semilinear problems. We are interested in results of local and global well posedness of autonomous and nonautonomous problems as well as the existence of global attractors (pullback) for several problems included in the class of semilinear problems. Furthermore, whenever possible, we will study the continuity of the family of global attractors (pullback). (AU)

Scientific publications

(6)

(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)

NASCIMENTO, MARCELO; PELICER, MAURICIO; PICOLLI, IAGO. LONG-TIME BEHAVIOR FOR FRACTIONAL WAVE EQUATIONS GOVERNED BY BI-HARMONIC OPERATOR. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 29, n. 6, p. 20-pg., 2023-11-23. (20/14075-6, 22/16305-4)

CUI, HONGYONG; FIGUEROA-LOPEZ, RODIAK N.; LANGA, JOSE A.; NASCIMENTO, MARCELO J. D.. Forward Attraction of Nonautonomous Dynamical Systems and Applications to Navier-Stokes Equations. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 23, n. 3, p. 37-pg., 2024-01-01. (20/14075-6, 22/16305-4)

FIGUEROA-LOPEZ, RODIAK N.; NASCIMENTO, MARCELO J. D.. Long-time behavior for evolution processes associated with non-autonomous nonlinear Schrödinger equation. Journal of Differential Equations, v. 386, p. 33-pg., 2024-01-04. (20/14075-6, 22/16305-4)

BELLUZI, MAYKEL B.; BEZERRA, FLANK D. M.; NASCIMENTO, MARCELO J. D.. On coupled semilinear evolution systems: Techniques on fractional powers of 4x4 matrices and applications. Mathematische Nachrichten, v. 297, n. 9, p. 25-pg., 2024-06-16. (22/01439-5, 20/14075-6, 22/16305-4)

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)

BELLUZI, MAYKEL; BEZERRA, FLANK D. M.; NASCIMENTO, MARCELO J. D.; SANTOS, LUCAS A.. A Higher-Order Non-autonomous Semilinear Parabolic Equation. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 55, n. 1, p. 17-pg., 2024-03-01. (22/01439-5, 20/14075-6, 22/16305-4)