Seminários ministrados online
Data: 7/04/2020
Horário: 17:00
Data: 07/04/2020
Palestrante: Márcio Cavalcante de Melo - UFAL
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/marcio-20
Título: Asymptotic stability of KdV solitons on the half-line
Resumo: In this talk I will discuss the asymptotic stability problem for KdV solitons on right half-line. Unlike standard KdV, these are not exact solutions to the equations posed on the half-line, and, contrary to NLS, no exact soliton solution seems to exist. In a previous result, we showed that solitons of the KdV equation posed in the entire line, placed sufficiently far from the origin, are stable in the half-line energy space, and assuming homogeneous boundary conditions. Now, we confirm these half-line KdV solitons are indeed asymptotically stable in the energy space. For the proof we follow in spirit the ideas by Martel and Merle, with some important differences coming from the fact that mass and energy are not conserved by the dynamics of the half-line KdV, and high regularity boundary terms modify the dynamics in the long time regime. Additionally, some bad behavior of the KdV soliton for the entire line must be cut off in order to ensure the correct convergence of the dynamics to a unique final state. This is a joint work with Claudio Muñoz (Universidad de Chile).
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Data: 14/04/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Renata Oliveira Figueira - UFSCar
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Well-posedness of the "good" Boussinesq equation with Gevrey initial data and time regularity
Resumo: We shall consider the Cauchy problem for the "good" Boussinesq equation with initial data belonging in a class of Gevrey functions on both the line and the circle, which includes a class of analytic function that can be extended holomorphically in a symmetric strip of the complex plane around the x-axis.
This talk is devoted to present a result about well-posedness in these classes of functions, which guarantees the Gevrey regularity of the solutions in space variable.
Also, we shall discuss the time regularity of the solution obtained.
This work is in collaboration with Rafael Barostichi and Alex Himonas.
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Data: 21/04/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Gabriel Cueva Candido Soares de Araújo - ICMC/USP
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Global regularity and solvability of linear differential operators on compact manifolds
Resumo: We will discuss some results, old and new, on global properties of differential operators on compact manifolds: solvability, hypoellipticity and related properties, both in the smooth and the analytic setup, as well as the relationships among them.
I will also show a few recent results of mine about operators on Lie groups (which generalize some results of Greenfield and Wallach on the torus) and also operators defined on spaces subject to more general group actions (in collaboration with Igor A. Ferra (UFABC) and Luis F. Ragognette (UFSCar)).
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Data: 28/04/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Ailton Campos do Nascimento
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Propagation of Regularity for Solutions of 2D Nonlinear Dispersive Models
Resumo: In this work we study special properties of solutions to nonlinear dispersive equations.
We establish the propagation of regularity phenomena for solutions of the initial value problem (IVP) associated to some 2D Nonlinear Dispersive Models namely, the fifth order Kadomtsev-Petviashvili II (KP5 -II) and the Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK) equations.
We prove that if initial data has some prescribed regularity on the right hand side of the real line, then this regularity is propagated with infinite speed by the flow solution. In other words, the extra regularity on the data propagates in the solutions in the direction of the dispersion.
The method of proof to obtain our result uses weighted energy estimates arguments combined with the smoothing properties of the solutions. Hence we need to have local well-posedness of the associated IVP via compactness method. In particular, we establish a local well-posedness theory for the BO-ZK equation which coincides with the best available in the literature proved employing more sophisticated tools.
We also discuss some open problems and other related results recently obtained for KP-BO and Shrira equation.
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Horário da palestra: 17:00
Palestrante: Brayan Mauricio Rodríguez Garzón (UFRJ)
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Mixing Exponential Lower bounds for the transport equation with L^2 initial data
Resumo:
We prove an exponential lower bound for the ||ρ(x, t)||_{H^{−1}} norm where ρ(x, t) is the solution of the transport equation with a vector field W^{1,p}(T^2) for 2 < p < ∞ and initial data ρ^0 ∈ L^2(T^2). We use the Monge-Kantorovich-Rubinstein distance as measure of mixing. We obtain constants depending only on ||ρ^0||_{L^2} and on the gradient of ln −concave function.
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Data: 12/05/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Vernny Chavez Ccajma (UFRJ)
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Homogenization of Schrödinger equations. Extended Effective Mass Theorems for non-crystalline matter
Resumo:
In this talk, we study the homogenization of the Schrödinger equation beyond the periodic setting. Rigorous derivation of the effective mass theorems in solid state physics for non crystalline materials are obtained. We prove that the solution is approximately the product of a fast oscillating eigenfunction and a slowly varying solution of an homogenized Schrödinger equation. This is a joint work with Wladimir Neves at UFRJ and Jean Silva at UFMG.
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Data: 19/05/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Luis Fernando Ragognette (UFSCar)
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Global hypoellipticity of sums of squares on compact manifolds
Resumo:
The goal of this talk is to introduce some classical and new results concerning hypoellipticity to a general audience.
Our plan is to discuss some famous results on local and global hypoellipticity of class of operators called sum of squares and, in
the last part of the talk, I will show some recent results obtained in collaboration with Gabriel Araújo (ICMC/USP) and Igor Ferra (UFABC).
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Data: 26/05/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Mykael Cardoso (UFPI)
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: On well-posedness and concentration of blow-up solutions for the intercritical inhomogeneous NLS equation
Resumo:
In this talk, we consider the focusing inhomogeneous nonlinear Schrödinger (INLS) equation in $R^n$ . We discuss about the local well posedness in a homogeneous Sobolev space. Sufficient conditions for global existence of solutions in this spaces are also established, using a Gagliardo-Nirenberg type estimate. Finally, we show the criticalnorm concentration phenomenon for finite time blow-up solutions. Our approach is based on the compact embedding of homogeneous Sobolev spaces into a weighted L p space. This is a joint work with Luiz Gustavo farah (UFMG) and Carlos M. Guzmán (UFF).
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Data: 02/06/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Joel Rogelio Portada Coacalli
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: $ L^2 $-estimates for solvability of inhomogeneous $ \bar\partial_b $-equation.
Resumo:
The purpose of this presentation is to introduce the tangential Cauchy-Riemann operator $ \bar\partial_b $; and also to present the microlocal argument used to obtain $ L^2 $-estimates that guarantee the existence of solutions, as well as the existence of regular solutions in $ L^2 $-Sobolev spaces, to the inhomogeneous $\bar\partial_b$-equation. In the last part of the conference I will present recently obtained results on this topic, in collaboration with Andrew Raich.
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Data: 09/06/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Victor Hugo Falcão Francheto
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Espaços de Hardy Radial
Resumo:
Neste trabalho apresentaremos uma decomposição atômica via átomos radias para distribuições em um subespaço do espaço de Hardy radial. Tal decomposição atômica nos diz que se uma distribuição é radial e está neste subespaço, então possui uma decomposição atômica radial.
Este trabalho é uma extensão de um teorema publicado por R. R. Coifman e G. Weiss em [1] no qual os autores apresentam uma decomposição atômica para funções radiais $f \in H^{1}$ no qual os átomos dessa decomposição são funções radiais.
A decomposição atômica que tratamos neste trabalho nos fornece informações sobre a radialidade dos átomos para $0<p\leqslant 1$. Especificamente, definimos um espaço de Hardy radial maximal e demonstramos uma decomposição atômica para este espaço via átomos radiais.
Referência:
[1] R. R. Coifman e G. Weiss. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc., 83(4):569-645, 1977.
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Data: 23/06/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Patricia Yukari Sato Rampazo
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Global $L^q$-ultradifferentiable functions
Resumo:
The class of global Gevrey functions was introduced recently by Z. Adwan, G. Hoepfner and A. Raich, the elements in these spaces are defined in terms of its derivatives with estimates that depend on sequences. It is know that in the local case ultradifferentiable functions defined by sequences and weight functions are not always the same. The purpose of this presentation is to introduce the class of global ultradifferentiable functions according with weight functions, and also to present some results such as a version of Paley-Wiener theorem.
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Data: 30/06/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Carlos Guzman Jimenez (UFF).
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: On the inhomogeneous NLS equation with inverse-square potential
Resumo:
We consider the inhomogeneous nonlinear Schrödinger equation with inverse quadratic potential, denoted by, (INLS_a).
i u_t + L_a u + |x|^{-b} |u|^\alpha u = 0, where L_a=- ∆ +a |x|^2.
In this talk we discuss some results for (INLS_a) , such as local and global well posedness. To this end, we use the Fixed Point Theorem based on the Strichartz estimates. Moreover we also discuss the scattering problem.
This is a joint work with Luccas Campos (UFMG).
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Data: 07/07/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Isnaldo Isaac Barbosa
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: THE NONLINEAR QUADRATIC INTERACTIONS OF THE SCHRODINGER ̈TYPE ON THE HALF-LINE
Resumo:
In this work we study the initial boundary value problem associated with the coupled Schrödinger equations with quadratic nonlinearities, that appears in nonlinear optics, on the half-line. We obtain the local well-posedness for data in Sobolev spaces with low regularity, by using a forcing problem on the full line with a presence of a forcing term in order to apply the Fourier restriction method of Bourgain. The crucial point in this work is the new bilinear estimates on the classical Bourgain spaces $X^{s,b}$ with $b<\frac12$. Here the understanding of the dispersion relation is the key point in theses estimates, where this relation clarify the notion of the resonant and the non resonant case.
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Data: 14/07/2020
Horário de entrada na sala: 16:50
Horário da palestra: 17:00
Palestrante: Max Reinhold Jahnke.
Local: Sala da Web Conferência RNP
link: https://conferenciaweb.rnp.br/webconf/renan-18
Título: Resolubilidade em grau máximo para estruturas hipocomplexas
Resumo:
Usamos a teoria da espaços duais de Fréchet-Schwartz (DFS) para estabelecer uma condição suficiente para resolubilidade em grau máximo para o complexo associado a estruturas localmente integráveis hipocomplexas. Como aplicação, provamos que a cohomologia em grau máximo de estruturas hipocomplexas invariantes à esquerda em grupos de Lie compactos podem ser calculadas usando apenas formas invariantes à esquerda, assim reduzindo o cálculo da cohomologia a um problema puramente algébrico