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Existência global para a equação periódica e dispersiva de Hunter-Saxton
(Universidade Federal de São Carlos, 2021-03-15)
In this master's thesis, we study the recent results about global existence for the integrable dispersive Hunter–Saxton equation in a periodic domain. Firstly, the local well-posedness of the Cauchy problem of the equation ...
Sobre a metrizabilidade do espaço de R-lugares de um corpo de funções F com trdeg_R=1
(Universidade Federal de São Carlos, 2020-02-28)
The main purpose of this work is to study the metrizability of the space of R-places of a function field, with transcendence degree 1 over a real closed field. Specifically, we are going to present a necessary and sufficient ...
Dinâmica topológica do operador deslocamento com pesos
(Universidade Federal de São Carlos, 2020-04-20)
In the present work, we will do a study of linear dynamics of operators, focusing mainly on
the concepts of topological transitivity, hypercyclicity and chaoticity. At rst, we will deal
with non-linear dynamical systems ...
Invariantes de singularidades em característica positiva
(Universidade Federal de São Carlos, 2020-03-30)
This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}.
Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...
Atratores pullback para uma equação de difusão não autônoma com retardo
(Universidade Federal de São Carlos, 2020-03-12)
Our goal in this work is to study a nonautonomous parabolic differential equation. We are going to show some results about existence of pullback attractors for this type of problem and for the equation without the delay.
Hipoelipticidade global analítica e Gevrey de sublaplacianos sob condições Diofantinas
(Universidade Federal de São Carlos, 2022-09-22)
In this dissertation we consider the problem of global Gevrey regularity for a class of partial differential
operators in the form of a sum of squares of vector fields and we show that these operators are
globally Gevrey ...
Attractors for processes on time-dependent spaces
(Universidade Federal de São Carlos, 2022-04-12)
The goal of this master’s degree dissertation is to study the asymptotic behavior of non-autonomous
hyperbolic partial differential equations with time-dependent coefficients. In order to achieve that, we
introduce the ...
Fluxo de curvatura média e self-shrinkers
(Universidade Federal de São Carlos, 2020-06-12)
Mean curvature flow is a geometric flow that rises when evolving a hipersurface in the direction of its normal vector field with velocity at each point equal to the mean curvature at the very same point. As it is an evolution ...
Symmetric and non-symmetric Jack Functions
(Universidade Federal de São Carlos, 2020-05-29)
The goal of this dissertation is to present the theory of Jack functions from the standpoint of algebraic combinatorics. The presentation of symmetric functions is largely centred on the first chapter of MacDonald's ...
Teoria dos operadores integrais singulares
(Universidade Federal de São Carlos, 2020-04-28)
We present in this work some of the main results regarding the continuity in Lp and the definition almost everywhere of operators known as Singular Integrals, as well as some classic examples and applications. We have ...