CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduation at Engenharia Elétrica from Universidade Federal da Bahia (1999), master's at Mathematics from Universidade Estadual de Campinas (2002) and doctorate at Mathematics from Universidade Estadual de Campinas (2005). Has experience in Mathematics, focusing on Partial Differential Equations, acting on the following subjects: comportamento assíntótico, equações de navier-stokes, soluções auto-similares and espaços de lorentz. (Source: Lattes Curriculum)
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In this project we will address well-posedness and qualitative properties of nonlinear Partial Differential Equations (PDEs) distributed in the following groups: elliptic equations and systems; fluid dynamics equations; and hyperbolic and dispersive equations. We will analyze how initial and boundary conditions, properties of domains, nonlinearities, potentials and forcing terms, presenti…
This project has basically two parts. In the first, we approach partial differential equations (PDEs) in rough spaces, such as weighted-Lp spaces (and sum of them), Morrey spaces, pseudomeasure spaces, Besov spaces, Fourier-Besov spaces, Fourier-Besov-Morrey spaces, Herz type spaces, Besov-Morrey spaces, and investigate the issues of existence, uniqueness, symmetries, renormalization, sta…
In this project we will address the following kinds of nonlinear partial differential equations: Elliptic, parabolic with a singular nonlinearity, dispersive, and wave equation. We will study issues as existence of solutions without Sobolev regularity, nonradial self-similarity, invariance under certain kinds of rotations, blow-up, and asymptotic behavior. The basic strategy is to study t…
Our main aim in this project is to study possible singularity formation scenarios for a class of generalized dissipative surface quasi-geostrophic equations, in which global well-posedness or singularity in finite time are still open problems. Thus, our proposal is to obtain results about the exclusion of the self-similar blow-up scenario, and in case of non-exclusion, to obtain results a…
The purpose of this project is to study the theory of well-posedness for the Cauchy problem of the fractional radiative transfer equation for general data and also study the stability/asymptotic behavior of solutions for such partial differential equations (EDPs) of order $s\in(0,1)$. We discuss equations that serve as model for physical phenomena associated to wave propagation of high-f…
In this project we consider fluid models with biological interactions of chemotaxis type. We analyse issues such as existence, uniqueness, formation of singularities, solutions without regularity of Sobolev type, self-similarity, stability and asymptotic behavior. The basic strategy is to study the models in different functional spaces with low regularity that allow solutions with the des…
The proposal of this project is to study existence, uniqueness, symmetries, blow-up and stability/asymptotic behavior of solutions for partial differential equations (PDEs) of order higher than $2$ (higher-order PDEs, for short). We address equations that model large-amplitude oscillations in bridges (PDEs of hyperbolic type with damping) and elliptic and parabolic PDEs with the polyharmo…
In this project we are interested in estimates of dispersive and Strichartz type for linear wave equations with time-dependent propagation of speed, mass and dissipation. We will assume suitable regularity and a sufficient control of the oscillations as $t\to\infty$. The interaction of the time-dependent coefficients will be analyzed to control its bad influence on the asymptotic profile …
(Only some records are available in English at this moment)
Our primary goal in this project is to investigate the stability of global minimizers among solutions of gradient flow equations for a broad class of two-dimensional anisotropic interaction energies, in which Riesz¿type singular repulsive kernels are coupled with a smooth confining potential and a directional weight that governs anisotropy. We aim to describe under which conditions, depen…
The purpose of this project is to study time periodic solutions for the inviscid generalized surface quasi-geostrophic equations and a 1D transport equation with nonlocal velocities. We intend to obtain the existence of non trivial rotating and traveling vortex patches by suitable perturbation of stationary solutions. The construction of those special solutions are done through a combi…
This project is intended to the study of recent developments in the theory of optimal transport and its applications to nonlinear nonlocal partial differential equations. These equations arise from systems where there exists conservation of mass and where the individuals of the system maintain an interaction among themselves. In some cases, the model can be identified as a gradient flow o…
| 3 / 3 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 10 / 9 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 2 / 2 | Completed scholarships abroad |
| 18 / 17 | All research grants and scholarships |
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