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Existência global de soluções para certos sistemas parabólicos não lineares
(Universidade Federal de São Carlos, 2005-03-02)
In this work, we study the global existence of smooth solutions for certain
systems of the form ut + f(u)x = Duxx, where u and f are vectors and D
is a positive, constant and diagonalizable matrix. We assume that the ...
Existência de soluções para uma classe geral de operadores do tipo p&q-Laplacianos
(Universidade Federal de São Carlos, 2021-08-26)
In this work, we will study the existence of non-trivial weak solutions for two classes
of elliptic and nonlinear problems, whose growth condition on these nonlinearities is
subcritical and which involve general operators ...
Ordinary and twisted K-theory
(Universidade Federal de São Carlos, 2022-03-28)
The main topic of this thesis consists in Ordinary and Twisted Topological K-Theory. We begin by describing generalized cohomology theories through the Eilenberg-Steenrod Axioms, in order to set Ordinary K-Theory in these ...
Leis de conservação: teoria geral
(Universidade Federal de São Carlos, 2022-03-24)
In this thesis we study some aspects of the theory of Partial Differential Equations (PDE's), the theory of the existence and the uniqueness of classical solutions to the Cauchy problem u_t+f'(u)u_x=0, u(0,x)=u_0(x) in the ...
Operadores de Calderón-Zygmund e o Teorema T(1)
(Universidade Federal de São Carlos, 2021-05-26)
The purpose of this work is to present, in a detailed way, one of the main topics of Harmonic Analysis: the singular integral operators or, in its general form, the Calderón-Zygmund operators. We did here, for the most ...
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 ...
Espectro do Laplaciano de Dirichlet-Neumann em faixas estreitas
(Universidade Federal de São Carlos, 2020-08-11)
Let $\Omega_\varepsilon$ be a thin strip in $\mathbb{R}^2$ and $-\Delta_{DN}^{\Omega_\varepsilon}$ the Dirichlet-Neumann Laplacian in $\Omega_\varepsilon$. In this work, we study the spectral problem of $-\Delta_{DN}^{\O ...
Fecho integral de módulos, multiplicidades e poliedros de Newton
(Universidade Federal de São Carlos, 2022-08-03)
In this work, we study the integral closure of ideals, Newton polyhedra and Newton non-degenerate ideals. Moreover, we present generalizations of these concepts for modules then, we study the characterization of Newton ...
Grupos de tranças de superfícies e espaços de recobrimento
(Universidade Federal de São Carlos, 2021-08-09)
Given M a compact and connected surface without boundary, we define the braid groups of M, denoted by B_n(M), geometrically. We also explore its relation with the configuration space and the mapping class group of the same ...
Soluções singulares para operadores diferenciais parciais com coeficientes constantes.
(Universidade Federal de São Carlos, 2004-02-26)
The objective of this work is to present some properties of singular solutions for linear partial differential operators with constant coe±cients. We prove Paley-Wiener-Schwartz s theorem and its version for singular ...