Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure

Existence of weak solutions for the generalized Navier-Stokes equations with damping

In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio

SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results

Timing of singleton births by onset of labour and mode of birth in NHS maternity units in England, 2005-2014: A study of linked birth registration, birth notification, and hospital episode data

BACKGROUND: Maternity care has to be available 24 hours a day, seven days a week. It is known that obstetric intervention can influence the time of birth, but no previous analysis at a national level in England has yet investigated in detail the ways in which the day and time of birth varies by onset of labour and mode of giving birth. METHOD: We linked data from birth registration, birth notification, and Maternity Hospital Episode Statistics and analysed 5,093,615 singleton births in NHS maternity units in England from 2005 to 2014. We used descriptive statistics and negative binomial regression models with harmonic terms to establish how patterns of timing of birth vary by onset of labour, mode of giving birth and gestational age. RESULTS: The timing of birth by time of day and day of the week varies considerably by onset of labour and mode of birth. Spontaneous births after spontaneous onset are more likely to occur between midnight and 6am than at other times of day, and are also slightly more likely on weekdays than at weekends and on public holidays. Elective caesarean births are concentrated onto weekday mornings. Births after induced labours are more likely to occur at hours around midnight on Tuesdays to Saturdays and on days before a public holiday period, than on Sundays, Mondays and during or just after a public holiday. CONCLUSION: The timing of births varies by onset of labour and mode of birth and these patterns have implications for midwifery and medical staffing. Further research is needed to understand the processes behind these findings

Why Give Birth in Health Facility? Users' and Providers' Accounts of Poor Quality of Birth Care in Tanzania.

In Tanzania, half of all pregnant women access a health facility for delivery. The proportion receiving skilled care at birth is even lower. In order to reduce maternal mortality and morbidity, the government has set out to increase health facility deliveries by skilled care. The aim of this study was to describe the weaknesses in the provision of acceptable and adequate quality care through the accounts of women who have suffered obstetric fistula, nurse-midwives at both BEmOC and CEmOC health facilities and local community members. Semi-structured interviews involving 16 women affected by obstetric fistula and five nurse-midwives at maternity wards at both BEmOC and CEmOC health facilities, and Focus Group Discussions with husbands and community members were conducted between October 2008 and February 2010 at Comprehensive Community Based Rehabilitation in Tanzania and Temeke hospitals in Dar es Salaam, and Mpwapwa district in Dodoma region. Health care users and health providers experienced poor quality caring and working environments in the health facilities. Women in labour lacked support, experienced neglect, as well as physical and verbal abuse. Nurse-midwives lacked supportive supervision, supplies and also seemed to lack motivation. There was a consensus among women who have suffered serious birth injuries and nurse midwives staffing both BEmOC and CEmOC maternity wards that the quality of care offered to women in birth was inadequate. While the birth accounts of women pointed to failure of care, the nurses described a situation of disempowerment. The bad birth care experiences of women undermine the reputation of the health care system, lower community expectations of facility birth, and sustain high rates of home deliveries. The only way to increase the rate of skilled attendance at birth in the current Tanzanian context is to make facility birth a safer alternative than home birth. The findings from this study indicate that there is a long way to go

Male partner attendance of skilled antenatal care in peri-urban Gulu district, Northern Uganda

<p>Abstract</p> <p>Background</p> <p>Male partner attendance of skilled Antenatal Care (ANC) is beneficial to improving maternal outcomes. This study investigated the level, perceived benefits and factors associated with male partner attendance of skilled ANC in a peri-urban community recovering from two decades of civil conflict.</p> <p>Methods</p> <p>This cross-sectional survey used multi-stage sampling in 12 villages of Omoro county to select 331 married male respondents aged 18 years or more, whose female spouses had childbirth within 24 months prior to the survey. A structured questionnaire elicited responses about male partner attendance of ANC during pregnancy at a public health facility as the main outcome variable. Analysis used Generalized Linear Model (GLM) in Stata version 10.0 to obtain Prevalence Risk Ratios (PRR) for association between the binary outcome and independent factors. All factors significant at p < 0.15 and potential confounders were included in the multivariable model.</p> <p>Results</p> <p>Overall, 65.4% (95%CI; 60.3, 70.5) male partners attended at least one skilled ANC visit. Mean age was 31.9 years [SD 8.2]. Perceived benefits of attending ANC were: HIV screening (74.5%), monitoring foetal growth (34%) and identifying complications during pregnancy (18.9%). Factors independently associated with higher ANC attendance were: knowledge of 3 or more ANC services (adj.PRR 2.77; 95%CI 2.24, 3.42), obtaining health information from facility health workers (adj.PRR 1.14; 95%CI 1.01, 1.29) and if spouse had skilled attendance at last childbirth (adj.PRR 1.31; 95%CI 1.04-1.64). However, factors for low attendance were: male partners intending their spouse to carry another pregnancy (adj.PRR 0.83; 95%CI 0.71, 0.97) and living more than 5 Km from a health facility (adj.PRR 0.83, 95%CI 0.70, 0.98).</p> <p>Conclusions</p> <p>Men who were knowledgeable of ANC services, obtained health information from a health worker and whose spouses utilised skilled delivery at last pregnancy were more likely to accompany their spouses at ANC, unlike those who wanted to have more children and lived more than 5 km from the health facility. These findings suggest that empowering male partners with knowledge about ANC services may increase their ANC participation and in turn increase skilled delivery. This strategy may improve maternal health care in post conflict and resource-limited settings.</p