O problema de existencia de soluções para a equação de Schrodinger não linear

Orientador: Marcia A. G. ScialomDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientíficaResumo: Neste trabalho estudamos a existência de soluções locais e globais para a equaçã.o de Schrodinger não linear (NLS). No primeiro capítulo apresentamos as ferramentas bá.sicas para posteriormente no capítulo dois fazermos um estudo da equação de Schrodinger homogênea. Estudamos também as propriedades dispersivas dessa equação, que serve para tratar a (NLS). Finalmente no capítulo três estudamos o problema de valor inicial associado à (NLS); demonstramos que sob certas hipóteses o problema é localmente bem posto e que sua solução nem sempre pode ser extendida globalmente.Abstract: Not informedMestradoMestre em Matemátic

Hartman-Grobman Theorems along Hyperbolic Stationary Trajectories

We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems

Climate dynamics and fluid mechanics: Natural variability and related uncertainties

The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change projections. To illustrate the first point, we focus on the large-scale, wind-driven flow of the mid-latitude oceans which contribute in a crucial way to Earth's climate, and to changes therein. We study the low-frequency variability (LFV) of the wind-driven, double-gyre circulation in mid-latitude ocean basins, via the bifurcation sequence that leads from steady states through periodic solutions and on to the chaotic, irregular flows documented in the observations. This sequence involves local, pitchfork and Hopf bifurcations, as well as global, homoclinic ones. The natural climate variability induced by the LFV of the ocean circulation is but one of the causes of uncertainties in climate projections. Another major cause of such uncertainties could reside in the structural instability in the topological sense, of the equations governing climate dynamics, including but not restricted to those of atmospheric and ocean dynamics. We propose a novel approach to understand, and possibly reduce, these uncertainties, based on the concepts and methods of random dynamical systems theory. As a very first step, we study the effect of noise on the topological classes of the Arnol'd family of circle maps, a paradigmatic model of frequency locking as occurring in the nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the seasonal cycle. It is shown that the maps' fine-grained resonant landscape is smoothed by the noise, thus permitting their coarse-grained classification. This result is consistent with stabilizing effects of stochastic parametrization obtained in modeling of ENSO phenomenon via some general circulation models.Comment: Invited survey paper for Special Issue on The Euler Equations: 250 Years On, in Physica D: Nonlinear phenomen

Versões aleatorias para o teorema de Hartman-Grobman

Orientador: Paulo R. C. RuffinoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Neste trabalho, apresentamos versões aleatórias discretas e contínuas do teorema de Hartman-Grobman da teoria qualitativa das equações diferenciais ordinárias. Especificamente, considere a equação diferencial autônoma em |Rm: x = f{x), onde f é um campo vetorial C1 , se f(t,x) é a solução desta equação não linear e F(t,x) = eDf(p) ^ tx é o fluxo solução da sua linearização em um ponto fixo hiperbólico p, o célebre teorema de Hartman-Grobman nos garante a existência de uma conjugação local desses fluxos: existe um homeomorfismo local h tal que eDf(p) ^ th(x) = h o f (t,x). No Capítulo 2 estudamos uma versão para difeomorfismos aleatórios deste teorema. Neste trabalho, diferente da abordagem de T. Wanner ("Lineariza-tion of random dynamical systeins", In Dynamics Reported, Vol. 4, Springer, 1994), adaptamos a demonstração do caso determinístico dada em Palis-Melo (Introdução aos Sistemas Dinâmicos. Projeto Euclides, CNPq, 1977). No Capítulo 3 estudamos uma versão estocástica para o teorema de Hartman-Grobman para campos vetoriais, i.e. considerando o fluxo de difeomorfismos ip{t,u,x) gerado por equações diferenciais estocásticas. Fica ainda em aberto, neste caso, a questão da inversibilidade de h(w). No Capítulo 4, motivados por Hartman ("On local homeomorphisms of Euclidean spaces", Boi Soe. Math. Mexicana, 5, 1960) estudamos a questão da diferenciabilidade do homeomorfismo h (üj) que realiza a conjugação.Abstract: Not informed.DoutoradoDoutor em Matemátic

Nonuniform laminated beam of Lord–Shulman type

The nonuniform thermoelastic laminated beam of the Lord–Shulman type is considered. The model is a two-layered beam with structural damping due to the interfacial slip. The well-posedness is proved by the semigroup theory of linear operators approach together with the Lumer–Phillips theorem. The stability results presented in this paper depend on the nature of a stability function (Formula presented.), which we define in (12). We first prove the lack of exponential stability of the system if (Formula presented.), (Formula presented.). And then, we establish the exponential stability for (Formula presented.) and polynomial decay with rate (Formula presented.) provided (Formula presented.), (Formula presented.). The result is new, and it is the first time that the nonuniform laminated beam is considered

O modelo epidemiológico SIRD aplicado à disseminação de COVID-19 na região peruana de Tacna

In the present research, the epidemiological model SIRD was used to study the spreed of the COVID-19 Pandemic in the Tacna Region. To determine the parameters of the model, the information published through social networks by the Regional Health Directorate of the Tacna Region of Peru was used, which was systematized in an EXCEL matrix and then exported to process the information in the System of Scientific Computing Mathematica. As a result, the graphs corresponding to the model referred to the Susceptible, Infected, Recovered and Deceased individuals from the COVID-19 Pandemic in the Tacna Region were obtained and then the graphs were interpreted in the time interval of the study. Keywords: COVID-19, SIRD epidemiologic model.En la presente investigación se usó el modelo epidemiológico SIRD para estudiar la propagación de la Pandemia COVID-19 en la Región de Tacna. Para determinar los parámetros del modelo se usó la información que publicó a través de redes sociales la Dirección Regional de Salud de la Región de Tacna del Perú, la cual se sistematizó en una matriz EXCEL y luego se exportó para procesar la información en el Sistema de Computación Científica Mathematica. Como resultado se obtuvo los gráficos correspondientes al modelo referidos a los individuos Susceptibles, Infectados, Recuperados y Fallecidos de la Pandemia del COVID-19 en la Región de Tacna y luego se interpretó los gráficos en el intervalo de tiempo del estudio. Palabras Claves: COVID-19, modelo epidemiológico SIRD