A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

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

Dunkl-Schrödinger Equations with and without Quadratic Potentials

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.

Global Results for Solution to the Mass-Critical Schrödinger Equation with Convolution Nonlinearity in R^n

Георги Венков, Христо Генев - Разглеждаме един клас от L^2 - критични нелинейни уравнения на Шрьодингер в R^(1+n) с конволюционна нелинейност от тип Хартри. Целта ни е да установим локалното и глобално съществуване на решенията, както и коректност на задачата на Коши в достатъчно малка околност на нулата в пространството L^2 (R^n). Като естествено следствие на глобалните резултати ние доказваме съществуване на оператор на разсейване за малки начални условия.

Can Early Intervention Policies Improve Well-being? Evidence from a randomized controlled trial

Many authors have proposed incorporating measures of well-being into evaluations of public policy. Yet few evaluations use experimental design or examine multiple aspects of well-being, thus the causal impact of public policies on well-being is largely unknown. In this paper we examine the effect of an intensive early intervention program on maternal well-being in a targeted disadvantaged community. Using a randomized controlled trial design we estimate and compare treatment effects on global well-being using measures of life satisfaction, experienced well-being using both the Day Reconstruction Method (DRM) and a measure of mood yesterday, and also a standardized measure of parenting stress. The intervention has no significant impact on negative measures of well-being, such as experienced negative affect as measured by the DRM and global measures of well-being such as life satisfaction or a global measure of parenting stress. Significant treatment effects are observed on experienced measures of positive affect using the DRM, and a measure of mood yesterday. The DRM treatment effects are primarily concentrated during times spent without the target child which may reflect the increased effort and burden associated with additional parental investment. Our findings suggest that a maternal-focused intervention may produce meaningful improvements in experienced well-being. Incorporating measures of experienced affect may thus alter cost-benefit calculations for public policies.

Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Boa colocação da equação quase-geostrófica em Lp-fraco

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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)

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

Planeamento integrado de alta hospitalar nos idosos

RESUMO: O planeamento da alta hospitalar representa um momento crucial no internamento de pessoas idosas, que muitas vezes regressam ao domicílio com necessidades complexas ao nível dos cuidados. No entanto, não existe um planeamento de alta universal, tornando prioritário o desenvolvimento de estratégias nesse sentido. Após revisão de literatura foi formulado um modelo de análise, com as dimensões e indicadores críticos para a problemática em estudo. Objectivo: Este estudo teve como objectivo analisar as repercussões que um planeamento de alta hospitalar integrado pode ter na satisfação e no bem-estar dos doentes e famílias, tendo impacto ao nível da redução das reincidências hospitalares. Métodos: Foi seleccionada uma amostra no Serviço de Medicina 1B do Centro Hospitalar Lisboa Norte, dividida aleatoriamente em dois grupos. O grupo controlo teve um planeamento de alta de acordo com os padrões habituais, enquanto o grupo experimental foi alvo de um planeamento de alta integrado, com enfoque na informação e clarificação nos cuidados pós alta, e com recurso à entrega de um documento de orientação para a alta. Foi realizado um contacto telefónico de follow-up um mês após a alta, para realização de um questionário telefónico. Resultados: Os participantes do grupo experimental revelaram ter tendência para estar mais bem preparados para a alta hospitalar e regresso ao domicílio, valorizando de forma mais positiva o processo de internamento e alta, bem como a auto-percepção de bem-estar. Conclusões: Apesar da limitação da dimensão da amostra, os resultados apontam no sentido de que os procedimentos do planeamento integrado de alta hospitalar têm um impacto positivo ao nível da satisfação e sentimento de bem-estar global dos idosos no regresso ao domicílio, influenciando na redução das reincidências hospitalares.------------ ABSTRACT: The hospital discharge planning represents a crucial moment in the hospitalization of the elderly, whom very often return home with very complex caring needs. However, there is no universal discharge planning as such, thus becoming mandatory to develop planning strategies. Upon review of reference literature, an investigational model was developed, that features the key indicators and dimensions of the subject matter. Aim: The aim of this study was to analyze how hospital discharge planning promotes the satisfaction and well-being of patients and their families, reducing the number of hospital readmissions. Methods: A sample population was selected from the 1B Internal Medicine Service of Centro Hospitalar Lisboa Norte, which was divided in two random groups. The control group experienced a standard discharge, whereas the experimental group underwent a planned integrated discharge, which focused on the clarification of the post-discharge caring needs. A discharge guidance document was produced and handed to the patients. One month after discharge, a follow-up telephone call was made. Results: The experimental group turned out to be better prepared for hospital discharge and to return home, positively valuing hospitalization and hospital discharge, as well as their perception of their own well-being. Conclusions: The integrated hospital discharge planning had a positive impact on patient satisfaction and global well-being upon their return, and effectively reduced the number of hospital readmissions.