CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
bachelor's at Engenharia Elétrica (Ênfase em Eletrônica) from Universidade de São Paulo (1984), master's at Mathematics from Universidade de São Paulo (1987) and doctorate at Center for Dynamical Systems and Nonlinear Studies from Georgia Institute of Technology (1992). Has experience in Mathematics, focusing on Partial Differential Equations, acting on thjavascript:void(0)e following subjects: attractors, atratores, parabolic problems, pullback attractors and problemas parabólicos. (Source: Lattes Curriculum)
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The dynamical systems that we seek to understand are those derived from differential equations in Banach spaces, which includes ordinary differential equations and partial semilinear (or quasilinear) evolutionary differential equations. The treatment that we give to these models has its origin in the spectral theory, via operational calculus, semigroup theory of linear operators and the v…
(Only some records are available in English at this moment)
The main goal of this project is to study the fractal dimension and the Assouad dimension of attractors for autonomous and non-autonomous dynamical systems, considering that the study of the dimension of the attractor of a dynamical system allows us, in certain cases, to reduce the complexity of this attractor by relating it to a subset of a finite-dimensional Euclidean space.Our first ob…
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)
In this project we propose to study qualitative properties of solutions of quasi-linear problems. We are particularly interested in the study of the saddle point property (for autonomous or non-autonomous problems) under very general conditions that include mathematical models of relevant practical problems. (AU)
(Only some records are available in English at this moment)
This project aims to study the topics of spectral theory of operators, theory of semigroups and their generators and geometric theory of parabolic semilinear differential equations, and then to apply such knowledge to analyze the semilinear Chafee-Infante equation. Finally, we seek to study stability and hyperbolicity of equilibria for a non-local quasilinear Chafee-Infante equation, maki…
We will see that the proposal developed mainly addresses qualitative issues associated with the study of the existence and characterization of the global attractor structure for some classes of nonlinear (autonomous and nonautonomous) parabolic problems with the presence of a Kirchhoff term in the operator. To solve such problems, we propose to combine variational and topological techniqu…
The aim of this project is to study and relate the concepts of non-autonomous attractors (pullback, uniform and skew-product), study results that give sufficient conditions for existence of non-autonomous attractors, study the Morse Decomposition of non-autonomous attractors and apply the theoretical results to the study of a model (discrete Chafee-Infante like), completely characterizing…
(Only some records are available in English at this moment)
This research project deals with the study of the dynamics of solutions, and the estimation of thefractal dimension of the attractors associated with a class of non-linear parabolic equations where the subdifferential main part is a non-linear maximal monotone operator and the convective term is a non-monotone, non-Lipschitz operator defined in a dense subset of a Hilbert space. The theor…
In this project we propose to study qualitative properties of solutions of quasi-linear problems. We are particularly interested in the study of shadowing and the saddle point property (for autonomous or non-autonomous problems) under very general conditions that include mathematical models of relevant practical problems and that do not satisfy the locally semilinear conditions usually im…
In this project, we are interested in finding non-autonomous equilibria and studying properties of stability and hyperbolicity related to those solutions aiming at characterizing the asymptotic dynamic of non-autonomous problems.
We study stochastic evolution equations, which are be obtain by perturbations with noises, autonomous evolution equations. We are interested in the asymptotic behavior of dresses equations and we search for results that a allow us to compare the autonomous problem with the stochastic problem obtain by perturbation. (AU)
For the research period abroad, I will study dynamical systems in infinite dimensions. I pretend to continue the studies that started in my Phd thesis at FU Berlin in 2017 and started at ICMC-USP in the same year. We will consider two problems described below. For such, I pretend to visit IST-Lisboa in order to contribute with the mathematics being done in Brazil, and increase the researc…
(Only some records are available in English at this moment)
| 2 / 2 | Ongoing research grants |
| 42 / 38 | Completed research grants |
| 4 / 4 | Ongoing scholarships in Brazil |
| 31 / 14 | Completed scholarships in Brazil |
| 2 / 2 | Ongoing scholarships abroad |
| 7 / 5 | Completed scholarships abroad |
| 88 / 65 | All research grants and scholarships |
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