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Universidade Federal de São Carlos (UFSCAR). Centro de Ciências Exatas e de Tecnologia (CCET)
(Institutional affiliation for the last research proposal)

Birthplace:
Brazil

bachelor's at Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (2000), master's at Mathematics from Universidade de São Paulo (2003) and doctorate at Mathematics from Universidade de São Paulo (2007). Has experience in Mathematics, focusing on Functional Analyses, acting on the following subjects: série de fourier, equações diferenciais parciais, equação do calor, informática na educação and análise funcional. (Source: Lattes Curriculum)

Research grants

- Study of non-autonomous semilinear parabolic ánd hyperbolic problems, AP.R
### 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. Add...

- Asymptotic behavior for non-autonomous semilinear problems, AP.R
### Abstract

The aim of this project is to study non-autonomous semilinear problems. We are interested in problems for which the unbounded operator depends on the temporal variable $t$, in general in the literature this dependence does not occur in the unbounded operator but in non-linearity. We will seek to obtain results of existence of pullback attractors for several problems included in this cla...

- Dynamics of autonomous and nonautonomous semilinear problems, AP.R
### Abstract

The aim of this project is to study evolution problems arising from semilinear equations, partial differential equations typically parabolic and hyperbolic semilinear autonomous or nonautonomous. We intend to consider semilinear partial differential equations (or nonlinear), involving an unbounded operator which is the infinitesimal generator of a C_0-semigroup (analytic or not). In the...

- Continuity of attractors to parabolic problems, AP.R
### Abstract

The aim of this project is to study the asymptotic behavior of autonomous and non-autonomous parabolic problems. Weintend to consider semilinear (or nonlinear) partial differential equations involving an unbounded operator which is the infinitesimalgenerator of a $C_0$-semigroup (analytic or not). In the non-autonomous case, the operator will depend on the time t,instead of the explicit...

Scholarships in Brazil

- Attractors for processes on time-dependent spaces, BP.MS
### Abstract

The main of this master's degree project is to study of non-autonomous parabolic/hyperbolic partial differential equations. We will study the notion of time-dependent attractor for process $U(t,\tau): X_{\tau} \to X_{t}$ exploiting the minimality with respect to the pullback attraction property. Finally, we will applied the abstract results to study the longterm behavior of wave equati...

- Pullback attractors for nonautonomous difusion equations with delay, BP.MS
### Abstract

The objective of this master's degree project is mainly focused on the study of non-autonomous parabolic partial differential equations. Let us consider semilinear partial differential equations, involving an unbounded operator (which explicitly depends on time $t$) that is an infinitesimal generator of an analytic semigroup. We will study the existence results of pullback attractor for...

- Introduction to Fourier analisys, BP.IC
### Abstract

The aim of this project is to provide the student basic knowledge of differential equations, giving you the opportunity to study a subject not covered in your grid disciplines of graduation. Let's apply the classical method of separation of variables for solving boundary value problems for treating some PDE's. (AU)

1 /
1
| Ongoing research grants |

3 /
3
| Completed research grants |

1 /
1
| Ongoing scholarships in Brazil |

5 /
2
| Completed scholarships in Brazil |

10 /
7
| All research grants and scholarships |

Associated processes |

(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)

Publications | 16 |

Citations | 49 |

Cit./Article | 3.1 |

Data from Web of Science |

BEZERRA, FLANK D. M.; PEREIRA, ANTONIO L.; DA SILVA, SEVERINO H.. Existence and continuity of global attractors and nonhomogeneous equilibria for a class of evolution equations with non local terms.** Journal of Mathematical Analysis and Applications**, v. 396, n. 2, p. 590-600, DEC 15 2012. Web of Science Citations: 8. (03/10042-0, 11/04166-5)

CARVALHO, ALEXANDRE N.; DLOTKO, TOMASZ; NASCIMENTO, MARCELO J. D.. Non-autonomous semilinear evolution equations with almost sectorial operators.** JOURNAL OF EVOLUTION EQUATIONS**, v. 8, n. 4, p. 631-659, 2008. Web of Science Citations: 9. (07/51373-0, 03/10042-0)

BEZERRA, FLANK D. M.; CARBONE, VERA L.; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. REGULARITY AND UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR A CLASS OF NONAUTONOMOUS THERMOELASTIC PLATE SYSTEMS.** PACIFIC JOURNAL OF MATHEMATICS**, v. 301, n. 2, p. 395-419, AUG 2019. Web of Science Citations: 0. (14/03686-3, 17/06582-2)

ARARUNA, FAGNER DIAS; MORAIS BEZERRA, FLANK DAVID. RATE OF ATTRACTION FOR A SEMILINEAR WAVE EQUATION WITH VARIABLE COEFFICIENTS AND CRITICAL NONLINEARITIES.** PACIFIC JOURNAL OF MATHEMATICS**, v. 266, n. 2, p. 257-282, DEC 2013. Web of Science Citations: 3. (11/04166-5)

BEZERRA, F. D. M.; CARVALHO, A. N.; CHOLEWA, J. W.; NASCIMENTO, M. J. D.. Parabolic approximation of damped wave equations via fractional powers: Fast growing nonlinearities and continuity of the dynamics.** Journal of Mathematical Analysis and Applications**, v. 450, n. 1, p. 377-405, JUN 1 2017. Web of Science Citations: 4. (14/03109-6, 03/10042-0, 14/03686-3)

DA SILVA, SEVERINO HORACIO; BEZERRA, FLANK D. M.. FINITE FRACTAL DIMENSIONALITY OF ATTRACTORS FOR NONLOCAL EVOLUTION EQUATIONS.** Electronic Journal of Differential Equations**, SEP 4 2013. Web of Science Citations: 3. (11/04166-5)

BEZERRA, F. D. M.; NASCIMENTO, M. J. D.; DA SILVA, S. H.. A class of dissipative nonautonomous nonlocal second-order evolution equations.** APPLICABLE ANALYSIS**, v. 96, n. 13, p. 2180-2191, 2017. Web of Science Citations: 2. (14/03109-6, 14/03686-3)

YANG, XIN-GUANG; NASCIMENTO, MARCELO J. D.; PELICER, MAURICIO L.. UNIFORM ATTRACTORS FOR NON-AUTONOMOUS PLATE EQUATIONS WITH p-LAPLACIAN PERTURBATION AND CRITICAL NONLINEARITIES.** DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS**, v. 40, n. 3, p. 1937-1961, MAR 2020. Web of Science Citations: 0. (17/06582-2)

BEZERRA, FLANK D. M.; CARVALHO, ALEXANDRE N.; NASCIMENTO, MARCELO J. D.. FRACTIONAL APPROXIMATIONS OF ABSTRACT SEMILINEAR PARABOLIC PROBLEMS.** DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B**, v. 25, n. 11, p. 4221-4255, SEP 2020. Web of Science Citations: 0. (03/10042-0, 14/03686-3, 17/06582-2)

BEZERRA, FLANK DAVID M.; NASCIMENTO, MARCELO JOSE D.. Convergence estimates of the dynamics of a hyperbolic system with variable coefficients.** MATHEMATICAL METHODS IN THE APPLIED SCIENCES**, v. 37, n. 5, p. 663-675, MAR 30 2014. Web of Science Citations: 1. (11/04166-5)

BEZERRA, FLANK D. M.; CARBONE, VERA L.; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. REGULARITY AND UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR A CLASS OF NONAUTONOMOUS THERMOELASTIC PLATE SYSTEMS.** PACIFIC JOURNAL OF MATHEMATICS**, v. 301, n. 2, p. 395-419, AUG 2019. Web of Science Citations: 0. (14/03686-3, 17/06582-2)

YANG, XIN-GUANG; NASCIMENTO, MARCELO J. D.; PELICER, MAURICIO L.. UNIFORM ATTRACTORS FOR NON-AUTONOMOUS PLATE EQUATIONS WITH p-LAPLACIAN PERTURBATION AND CRITICAL NONLINEARITIES.** DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS**, v. 40, n. 3, p. 1937-1961, MAR 2020. Web of Science Citations: 0. (17/06582-2)

BEZERRA, FLANK D. M.; CARVALHO, ALEXANDRE N.; NASCIMENTO, MARCELO J. D.. FRACTIONAL APPROXIMATIONS OF ABSTRACT SEMILINEAR PARABOLIC PROBLEMS.** DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B**, v. 25, n. 11, p. 4221-4255, SEP 2020. Web of Science Citations: 0. (03/10042-0, 14/03686-3, 17/06582-2)

BEZERRA, F. D. M.; CARVALHO, A. N.; CHOLEWA, J. W.; NASCIMENTO, M. J. D.. Parabolic approximation of damped wave equations via fractional powers: Fast growing nonlinearities and continuity of the dynamics.** Journal of Mathematical Analysis and Applications**, v. 450, n. 1, p. 377-405, JUN 1 2017. Web of Science Citations: 4. (14/03109-6, 03/10042-0, 14/03686-3)

ARARUNA, FAGNER DIAS; MORAIS BEZERRA, FLANK DAVID. RATE OF ATTRACTION FOR A SEMILINEAR WAVE EQUATION WITH VARIABLE COEFFICIENTS AND CRITICAL NONLINEARITIES.** PACIFIC JOURNAL OF MATHEMATICS**, v. 266, n. 2, p. 257-282, DEC 2013. Web of Science Citations: 3. (11/04166-5)

DA SILVA, SEVERINO HORACIO; BEZERRA, FLANK D. M.. FINITE FRACTAL DIMENSIONALITY OF ATTRACTORS FOR NONLOCAL EVOLUTION EQUATIONS.** Electronic Journal of Differential Equations**, SEP 4 2013. Web of Science Citations: 3. (11/04166-5)

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

NASCIMENTO, Marcelo José Dias. Problemas parabólicos selineares singularmente não autônomos com expoentes críticos. Tese (Doutorado) - Instituto de Ciências Matemáticas e de Computação. Universidade de São Paulo (USP). São Carlos. (02/11855-2)

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