We consider a system of nonlinear diffusion equations modelling (isothermal) phase segregation of an ideal mixture of
N
≥
2
components occupying a bounded region
Ω
⊂
R
d
,
d
≤
3
. Our system is ...subject to a constant mobility matrix of coefficients, a free energy functional given in terms of
singular entropy
generated potentials and
localized
capillarity effects. We prove well-posedness and regularity results which generalize the ones obtained by Elliott and Luckhaus (IMA Preprint Ser 887, 1991). In particular, if
d
≤
2
, we derive the uniform strict separation of solutions from the singular points of the (entropy) nonlinearity. Then, even if
d
=
3
, we prove the existence of a global (regular) attractor as well as we establish the convergence of solutions to single equilibria. If
d
=
3
, this convergence requires the validity of the asymptotic strict separation property. This work constitutes the first part of an extended three-part study involving the phase behavior of multi-component systems, with a second part addressing the presence of nonlocal capillarity effects, and a final part concerning the numerical study of such systems along with some relevant application.
The natural resistance of plants to disease is based not only on preformed mechanisms, but also on induced mechanisms. The defense mechanisms present in resistant plants may also be found in ...susceptible ones. This study attempted to analyze the metabolic alterations in plants of the potato Solanum tuberosum L. cv. Agata that were inoculated with the incompatible plant-pathogenic bacteria X. axonopodis and R. solanacearum, and the compatible bacterium E. carotovora. Levels of total phenolic compounds, including the flavonoid group, and the activities of polyphenol oxidase (PPO) and peroxidase (POX) were evaluated. Bacteria compatibility was evaluated by means of infiltration of tubers. The defense response was evaluated in the leaves of the potato plants. Leaves were inoculated depending on their number and location on the stem. Multiple-leaf inoculation was carried out on basal, intermediate, and apical leaves, and single inoculations on intermediate leaves. Leaves inoculated with X. axonopodis and with R. solanacearum showed hypersensitive responses within 24 hours post-inoculation, whereas leaves inoculated with E. carotovora showed disease symptoms. Therefore, the R. solanacearum isolate used in the experiments did not exhibit virulence to this potato cultivar. Regardless of the bacterial treatments, the basal leaves showed higher PPO and POX activities and lower levels of total phenolic compounds and flavonoids, compared to the apical leaves. However, basal and intermediate leaves inoculated with R. solanacearum and X. axonopodis showed increases in total phenolic compounds and flavonoid levels. In general, multiple-leaf inoculation showed the highest levels of total phenolics and flavonoids, whereas the single inoculations resulted in the highest increase in PPO activity. The POX activity showed no significant difference between single- and multiple-leaf inoculations. Plants inoculated with E. carotovora showed no significant increase in defense mechanisms such as enzyme activity and phenolic compounds. Therefore, resistance or susceptibility in S. tuberosum cv. Agata might depend on leaf age, type of inoculation performed (single or multiple), and the interaction between plant and pathogen.
This paper investigates how changes in expectations regarding the ability of the European Monetary Union to address the debt crisis have asymmetrically impacted the cost of sovereign borrowing in ...central and peripheral European countries. It shows that most of the variations in sovereign spreads can be explained by fundamentals in a model that allows for structural breaks. We test for both the presence and the time of structural breaks, deriving their asymptotic distribution and confidence intervals. The two estimated breakpoints are: the second quarter of 2010, a period when financial markets lacked confidence in a resolution for the crisis; and the third quarter of 2010, when financial markets regained confidence following Mario Draghi's 'whatever it takes' announcement. Market fears, measured by the degree of international risk aversion, became more important to price sovereign debt only for peripheral economies during the crisis.
In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensional setting. The ...control enters the governing state system in a nonlinear fashion in the form of a prescribed solenoidal, that is a divergence-free, vector field, whereas the cost functional to be minimized is of tracking-type. The novelties of the present paper are twofold: in addition to the control application, the intrinsic difficulties of the optimization problem forced us to first establish new regularity results on the nonlocal Cahn-Hilliard equation that were unknown even without the coupling with a velocity field and are therefore of independent interest. This happens to be shown using the recently proved separation property along with ad hoc Hölder regularities and a bootstrap method. For the control problem, the existence of an optimal strategy as well as first-order necessary conditions are then established.
The link between compressible models of tissue growth and the Hele–Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models, only repulsive ...forces and advection terms are taken into account. In order to take into account long range interactions, we include a surface tension effect by adding a nonlocal term which leads to the degenerate nonlocal Cahn–Hilliard equation, and study the incompressible limit of the system. The degeneracy and the source term are the main difficulties. Our approach relies on a new
L
∞
estimate obtained by De Giorgi iterations and on a uniform control of the energy despite the source term. We also prove the long-term convergence to a single constant stationary state of any weak solution using entropy methods, even when a source term is present. Our result shows that the surface tension in the nonlocal (and even local) Cahn–Hilliard equation will not prevent the tumor from completely invading the domain.
The 1994 United Nations International Conference on Population and Development (ICPD) identified the centrality of defending reproductive rights and the importance of ensuring voluntary reproductive ...choices (UNFPA, 2019). This paper presents a review of the main theoretical models of demand for children and, by assessing the empirical counterpart of these models in an international database, points out the main socioeconomic variables determining fertility. This study shows that female schooling is the most important socioeconomic variable to explain the number of children per woman, as increased female education can expand access to information on contraceptive methods, improve employment opportunities and “empower” women in defending their sexual and reproductive choices.
A Conferência Internacional sobre População e Desenvolvimento das Nações Unidas (CIPD) de 1994 identificou a centralidade da defesa dos direitos reprodutivos e a importância de se garantir a realização de escolhas reprodutivas voluntárias (UNFPA, 2019). O presente artigo apresenta uma revisão sobre os principais modelos teóricos de demanda por filhos e, avaliando a contrapartida empírica desses modelos em uma base de dados internacional, aponta as principais variáveis socioeconômicas determinantes da fecundidade. Esse estudo mostra que a escolaridade feminina é a variável socioeconômica mais importante para explicar o número de filhos por mulher, visto que o aumento da educação feminina pode expandir o acesso à informação sobre os métodos contraceptivos, melhorar as oportunidades de emprego e “empoderar” as mulheres na defesa de suas escolhas sexuais e reprodutivas.
La Conferencia Internacional de las Naciones Unidas sobre Población y Desarrollo (CIPD) de 1994 identificó la centralidad de defender los derechos reproductivos y la importancia de garantizar opciones reproductivas voluntarias (UNFPA 2019). Este artículo presenta una revisión de los principales modelos teóricos de demanda de niños y, al evaluar la contraparte empírica de estos modelos en una base de datos internacional, señala las principales variables socioeconómicas que determinan la fertilidad. Este estudio muestra que la escolarización femenina es la variable socioeconómica más importante para explicar el número de hijos por mujer, ya que una mayor educación femenina puede ampliar el acceso a la información sobre métodos anticonceptivos, mejorar las oportunidades de empleo y "empoderar" a las mujeres en defensa de sus elecciones sexuales y reproductivas.
We investigate the nonlocal version of the Abels-Garcke-Grün (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible ...Navier-Stokes-Cahn-Hilliard system characterized by concentration-dependent density and viscosity, and an additional flux term due to interface diffusion. In particular, the Cahn-Hilliard dynamics of the concentration (phase-field) is governed by the aggregation/diffusion competition of the nonlocal Helmholtz free energy with singular (logarithmic) potential and constant mobility. We first prove the existence of global strong solutions in general two-dimensional bounded domains and their uniqueness when the initial datum is strictly separated from the pure phases. The key points are a novel well-posedness result of strong solutions to the nonlocal convective Cahn-Hilliard equation with singular potential and constant mobility under minimal integral assumption on the incompressible velocity field, and a new two-dimensional interpolation estimate for the L4(Ω) control of the pressure in the stationary Stokes problem. Secondly, we show that any weak solution, whose existence was already known, is globally defined, enjoys the propagation of regularity and converges towards an equilibrium (i.e., a stationary solution) as t→∞. Furthermore, we demonstrate the uniqueness of strong solutions and their continuous dependence with respect to general (not necessarily separated) initial data in the case of matched densities and unmatched viscosities (i.e., the nonlocal model H with variable viscosity, singular potential and constant mobility). Finally, we provide a stability estimate between the strong solutions to the nonlocal AGG model and the nonlocal Model H in terms of the difference of densities.
Nous étudions la version non locale du système d'Abels-Garcke-Grün (AGG), qui décrit l'évolution d'un mélange de deux fluides incompressibles. Il est constitué du système de Navier-Stokes-Cahn-Hilliard incompressible caractérisé par des densités et viscosités dépendant de la concentration, et d'un terme de flux additionnel dû à la diffusion d'interface. En particulier, la dynamique de Cahn-Hilliard de la concentration (champ de phase) est gouvernée par la compétition aggrégation/diffusion de l'énergie libre de Helmholtz non locale avec potentiel singulier (logarithmique) et mobilité constante. Nous démontrons d'abord l'existence globale de solutions fortes dans un domaine borné de dimension deux, ainsi que leur unicité lorsque la donnée initiale est strictement séparée des phases pures. Les points clefs sont un nouveau résultat sur le caractère bien-posé de solutions fortes de l'équation de Cahn-Hilliard convective avec potentiel singulier et mobilité constante sous une hypothèse intégrale minimale sur le champ de vitesse incompressible et une nouvelle estimation d'interpolation en dimension deux pour le contrôle L4(Ω) de la pression dans le problème de Stokes stationnaire. Dans un deuxième temps, nous montrons que toute solution faible, dont l'existence est déjà connue, est définie globalement, propage la régularité et converge vers un équilibre (i.e., une solution stationnaire) lorsque t→∞. De plus, nous montrons l'unicité des solutions fortes et leur dépendance continue par rapport à des données initiales générales (pas nécessairement séparées) dans le cas de densités égales et viscosités différentes (i.e., the modèle H non local avec viscosité variable, potentiel singulier et mobilité constante). Finalement, nous donnons une estimation de stabilité entre les solutions fortes du modèle AGG non local et le modèle H non local en terme de la différence des densités.
A Conferência Internacional sobre População e Desenvolvimento das Nações Unidas (CIPD) de 1994 identificou a centralidade da defesa dos direitos reprodutivos e a importância de se garantir a ...realização de escolhas reprodutivas voluntárias (UNFPA, 2019). O presente artigo apresenta uma revisão sobre os principais modelos teóricos de demanda por filhos e, avaliando a contrapartida empírica desses modelos em uma base de dados internacional, aponta as principais variáveis socioeconômicas determinantes da fecundidade. Esse estudo mostra que a escolaridade feminina é a variável socioeconômica mais importante para explicar o número de filhos por mulher, visto que o aumento da educação feminina pode expandir o acesso à informação sobre os métodos contraceptivos, melhorar as oportunidades de emprego e “empoderar” as mulheres na defesa de suas escolhas sexuais e reprodutivas.
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