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

Stochastics and Dynamics

Texto completo: acesso restrito. p.497-508In this article we investigate the existence and uniqueness of strong solutions to the initial-boundary value problem with homogeneous boundary conditions for a stochastic nonlinear parabolic equation of nonlocal type with multiplicative white noise. Moreover, we prove a simple result on the asymptotic behavior for the solution

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

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

HARTMAN-GROBMAN THEOREMS ALONG HYPERBOLIC STATIONARY TRAJECTORIES

Abstract. We extend the Hartman-Grobman theorems for 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 travelling neighborhoods of trajectories and neighborhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems. 1. Introduction. The celebrated Hartman-Grobman theorem (HGT, for short) plays a fundamental rule in the theory of dynamical systems. Essentially, among other features, it allows one to make topological classification of the dynamics in a neighborhood of hyperbolic fixed points. This classification is based on the existence of a conjugacy of the local dynamics with the linearized system at a hyperbolic fixe

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trajectorie