Semigrupos de operadores lineares limitados: soluções Mild e Weak

Pós-graduação em Matemática - IBILCE

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth a, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. (C) 2011 Elsevier Ltd. All rights reserved.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

Boa colocação da equação quase-geostrófica em Lp-fraco

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Existência de soluções quase automórficas para equações diferenciais abstratas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Soluções quase automórficas para equações diferenciais abstratas de segunda ordem

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Boa colocação da equação do calor semilinear em L^p-fraco

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Boa colocação da equação do calor semilinear em L^p-fraco

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Wick product and Wong-Zakai approximations.

This thesis is a compilation of 6 papers that the author has written together with Alberto Lanconelli (chapters 3, 5 and 8) and Hyun-Jung Kim (ch 7). The logic thread that link all these chapters together is the interest to analyze and approximate the solutions of certain stochastic differential equations using the so called Wick product as the basic tool. In the first chapter we present arguably the most important achievement of this thesis; namely the generalization to multiple dimensions of a Wick-Wong-Zakai approximation theorem proposed by Hu and Oksendal. By exploiting the relationship between the Wick product and the Malliavin derivative we propose an original reduction method which allows us to approximate semi-linear systems of stochastic differential equations of the Itô type. Furthermore in chapter 4 we present a non-trivial extension of the aforementioned results to the case in which the system of stochastic differential equations are driven by a multi-dimensional fraction Brownian motion with Hurst parameter bigger than 1/2. In chapter 5 we employ our approach and present a “short time” approximation for the solution of the Zakai equation from non-linear filtering theory and provide an estimation of the speed of convergence. In chapters 6 and 7 we study some properties of the unique mild solution for the Stochastic Heat Equation driven by spatial white noise of the Wick-Skorohod type. In particular by means of our reduction method we obtain an alternative derivation of the Feynman-Kac representation for the solution, we find its optimal Hölder regularity in time and space and present a Feynman-Kac-type closed form for its spatial derivative. Chapter 8 treats a somewhat different topic; in particular we investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of semi-linear stochastic differential equations describing a predator-prey model perturbed by Gaussian noise.

Erosion-corrosion of mild steel in hot caustic. Part I: NaOH solution

A novel apparatus, high-pressure/high-temperature nickel flow loop, was constructed to study the effect of the flow on the rate of erosion-corrosion of mild steel in hot caustic. It has been successfully used to measure the corrosion rate of 1020 steel in 2.75 M NaOH solution at a temperature of 160 degrees C and velocities of 0.32 and 2.5 m/s. In situ electrochemical methods were used to measure the corrosion rate such as the potentiodynamic sweep, the polarization resistance method, and electrochemical impedance spectroscopy (EIS). Also used were the weight-loss method and scanning electron microscopy (SEM). Eight electrodes/coupons were used to monitor the metal loss rate, four were placed at the low velocity section, while the other four were placed in the high velocity section. The first three coupons in each section were placed within the disturbed flow region, while the fourth was placed in a fully developed flow region. The corrosion rate of the coupons in the high velocity section was generally higher than that of the coupons in the low velocity section. One coupon in the disturbed flow region had a significantly higher corrosion rate than the others. (c) 2005 Elsevier Ltd. All rights reserved.

Dodigen 213-N as corrosion inhibitor for ASTM 1010 mild steel in 10% HCL

This article describes a study of the behavior of a mixture of amines and amides, commercially known as Dodigen 213-N (D-213 N), as a corrosion inhibitor for ASTM 1010 mild steel in 10% w/w HCl solution. The concentration range used was 1 x 10(-5) M to 8 x 10(-4) M. The weight loss and electrochemical techniques used were corrosion potential measurement, anodic and cathodic polarization curves, and electrochemical impedance spectroscopy (EIS). The solution temperature was 50 +/- A 1 A degrees C and it was naturally aerated. The corrosion potential values shifted to slightly more positive values, thus indicating mixed inhibitor behavior. The anodic and cathodic polarization curves showed that D-213 N is an effective corrosion inhibitor, since both the anodic and the cathodic reactions were polarized in comparison with those obtained without inhibitor. For all concentrations the cathodic polarization curves were more polarized than the anodic ones. The inhibition efficiency was in the range 75-98%, calculated from values of weight loss and corrosion current density, i (corr), obtained by extrapolation of Tafel cathodic linear region.