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Estabilidade assintótica global para equações diferenciais no plano
(Universidade Federal de São Carlos, 1999-05-25)
Let x! = f(x) be a system of differential equations in the plane where / is C1. This work gives sufficient conditions which guarantee that the basin of attraction of an equilibrium point is the plane. This monograph reports ...
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 ...
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 ...
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 ...
Estabilidade de Standing waves
(Universidade Federal de São Carlos, 2014-03-13)
This work is concerned with the orbital stability of special solutions called "standing waves" for Hamiltonian systems in a real and invariant Hilbert space under the action of a specific group of isometries in such space. ...
On the classification of two dimensional flows
(Universidade Federal de São Carlos, 2023-08-02)
Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ...
Teorema da esfera suave via fluxo de Ricci
(Universidade Federal de São Carlos, 2023-08-04)
The goal of this dissertation is the theoretical development of the Ricci flow, a differential equation over a family of Riemannian metrics on an arbitrary differentiable manifold, and its use in the proof of the so-called ...