Study of non-autonomous semilinear parabolic and hyperbolic problems

• Grant number: 19/26841-8
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2020
• End date: May 31, 2022
• 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

Abstract

The main objective of this project is to study autonomous and non-autonomous parabolic and hyperbolic semilinear problems. We are interested in obtaining results of existence of pullback attractors for several problems included in this class of semilinear problems. Whenever possible, we will study the robustness of these objects (attractors) in the sense of continuity of attractors. Additionally, we consider parabolic approximations of hyperbolic problems. (AU)

Scientific publications

(8)

(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)

ARAGAO, GLEICIANE S.; BEZERRA, FLANK D. M.; FIGUEROA-LOPEZ, RODIAK N.; NASCIMENTO, MARCELO J. D.. Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients. Journal of Differential Equations, v. 298, p. 30-67, OCT 15 2021. (19/26841-8, 19/04476-6)

BELLUZI, MAYKEL; CARABALLO, TOMAS; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. trong solutions for semilinear problems with almost sectorial operator. JOURNAL OF EVOLUTION EQUATIONS, v. 22, n. 1, MAR 2022. (19/26841-8, 17/17502-0, 17/09406-0)

BELLUZI, MAYKEL; BEZERRA, FLANK D. M.; NASCIMENTO, MARCELO J. D.. ON SPECTRAL AND FRACTIONAL POWERS OF DAMPED WAVE EQUATIONS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 21, n. 8, p. 35-pg., 2022-04-22. (17/17502-0, 19/26841-8, 17/09406-0)

AZEVEDO, VINICIUS T.; BONOTTO, EVERALDO M.; CUNHA, ARTHUR C.; NASCIMENTO, MARCELO J. D.. Existence and stability of pullback exponential attractors for a nonautonomous semilinear evolution equation of second order. Journal of Differential Equations, v. 365, p. 39-pg., 2023-05-02. (19/26841-8, 20/14075-6)

BELLUZI, MAYKEL; CARABALLO, TOMAS; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. Smoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operators. Journal of Differential Equations, v. 314, p. 42-pg., 2022-01-24. (17/17502-0, 19/26841-8, 17/09406-0)

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)

BELLUZI, MAYKEL; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. On a cascade system of Schrodinger equations. Fractional powers approach. Journal of Mathematical Analysis and Applications, v. 506, n. 1, FEB 1 2022. (17/17502-0, 19/26841-8, 17/09406-0)

BONOTTO, EVERALDO M.; NASCIMENTO, MARCELO J. D.; SANTIAGO, ERIC B.. IMPULSIVE EVOLUTION PROCESSES: ABSTRACT RESULTS AND AN APPLICATION TO A COUPLED WAVE EQUATIONS. Advances in Differential Equations, v. 28, n. 7-8, p. 44-pg., 2023-07-01. (19/26841-8, 20/14075-6)