A Ginzburg-Landau type energy with weight and with convex potential near zero

In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower bound for the energy of unit vector field given initially by Brezis-Merle-Rivi\`ere

Optimal control for evolutionary imperfect transmission problems

We study the optimal control problem of a second order linear evolution equation defined in two-component composites with e-periodic disconnected inclusions of size e in presence of a jump of the solution on the interface that varies according to a parameter γ. In particular here the case $\gamma<1$ is analyzed. The optimal control theory, introduced by Lions (Optimal Control of System Governed by Partial Differential Equations, 1971), leads us to characterize the control as the solution of a set of equations, called optimality conditions. The main result of this paper proves that the optimal control of the e-problem, which is the unique minimum point of a quadratic cost functional $J_{\varepsilon}$ , converges to the optimal control of the homogenized problem with respect to a suitable limit cost functional $J_{\infty}$ . The main difficulties are to find the appropriate limit functional for the control of the homogenized system and to identify the limit of the controls

Uniform resolvent convergence for strip with fast oscillating boundary

In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change

Clinical features and outcomes of elderly hospitalised patients with chronic obstructive pulmonary disease, heart failure or both

Background and objective: Chronic obstructive pulmonary disease (COPD) and heart failure (HF) mutually increase the risk of being present in the same patient, especially if older. Whether or not this coexistence may be associated with a worse prognosis is debated. Therefore, employing data derived from the REPOSI register, we evaluated the clinical features and outcomes in a population of elderly patients admitted to internal medicine wards and having COPD, HF or COPD + HF. Methods: We measured socio-demographic and anthropometric characteristics, severity and prevalence of comorbidities, clinical and laboratory features during hospitalization, mood disorders, functional independence, drug prescriptions and discharge destination. The primary study outcome was the risk of death. Results: We considered 2,343 elderly hospitalized patients (median age 81&nbsp;years), of whom 1,154 (49%) had COPD, 813 (35%) HF, and 376 (16%) COPD + HF. Patients with COPD + HF had different characteristics than those with COPD or HF, such as a higher prevalence of previous hospitalizations, comorbidities (especially chronic kidney disease), higher respiratory rate at admission and number of prescribed drugs. Patients with COPD + HF (hazard ratio HR 1.74, 95% confidence intervals CI 1.16-2.61) and patients with dementia (HR 1.75, 95% CI 1.06-2.90) had a higher risk of death at one year. The Kaplan-Meier curves showed a higher mortality risk in the group of patients with COPD + HF for all causes (p = 0.010), respiratory causes (p = 0.006), cardiovascular causes (p = 0.046) and respiratory plus cardiovascular causes (p = 0.009). Conclusion: In this real-life cohort of hospitalized elderly patients, the coexistence of COPD and HF significantly worsened prognosis at one year. This finding may help to better define the care needs of this population

A Ginzburg–Landau Type Energy with Weight and with Convex Potential Near Zero

International audienc

Minimization of a quasi-linear Ginzburg-Landau type energy

International audienceLet G be a smooth bounded domain in R(2). Consider the functional E(epsilon) (u) = 1/2 integral(G) (p(0) + t |x|(k) |u|(t)) |del u|(2) + 1/4 epsilon(2) integral(G) (1-|u|(2))(2) on the set H(g)(1) (G, C) = {u is an element of H(1)(G, C): u = g on partial derivative G} where g is a given boundary data with degree d >= 0. In this paper we will study the behavior of minimizers u(epsilon) of E(epsilon) and we will estimate the energy E(epsilon) (u(epsilon)). (C) 2008 Elsevier Ltd. All rights reserved

Minimization of a Quasi-linear Ginzburg-Landau type energy

International audienceAbstract. We study an energy of Ginzburg Landau problem E(u) with a weight depending on x and on u

Homogenization of a Ginzburg-Landau problem in a perforated domain with mixed boundary conditions

In this paper we study the asymptotic behavior of a Ginzburg-Landau problem in a e-periodically perforated domain of with mixed Dirichlet-Neumann conditions. The holes can verify two different situations. In the first one they have size e and a homogeneous Dirichlet condition is posed on a flat portion of each hole, whose size is an order smaller than e, the Neumann condition being posed on the remaining part. In the second situation, we consider two kinds of e-periodic holes, one of size of order smaller than e, where a homogeneous Dirichlet condition is prescribed and the other one of size e, on which a non-homogeneous Neumann condition is given. Moreover, in this case as e goes to zero, the two families of holes approach each other. In both situations a homogeneous Dirichlet condition is also prescribed on the whole exterior boundary of the domain. MSC: 35J20, 35J25, 35B25, 35J55, 35B40