No abstract

We show that solutions of the chemical reaction-diffusion system associated to A + B C in one spatial dimension can be approximated in L 2 on any finite time interval by solutions of a space discretized ODE system which models the corresponding chemical reaction system replicated in the discretization subdomains where the concentrations are assumed spatially constant. Same-species reactions through the virtual boundaries of adjacent subdomains lead to diffusion in the vanishing limit. We show convergence of our numerical scheme by way of a consistency estimate, with features generalizable to reaction networks other than the one considered here, and to multiple space dimensions. In particular, the connection with the class of complex-balanced systems is briefly discussed here, and will be considered in future work. reaction-diffusion and method of lines and reaction networks MSC 35K57 and MSC 65M20 and MSC 35Q80 and MSC 80A30

We study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. Finally, we introduce the weaker concept of dissipative mild solutions and we show that in this case the surface-tension energy dissipation is the mechanism responsible for the H 1 -norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means.

principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream numerical tool and the specialized literature is rather scarce. The method amounts to discretizing evolutionary PDE's in space only, so it produces a semi-discrete numerical scheme which consists of a system of ODE's (in the time variable). To prove convergence of the semi-discrete MOL scheme to the original PDE one needs to perform some more or less traditional analysis: it is necessary to show that the scheme is consistent with the continuous problem, and that the discretized version of the spatial differential operator retains sufficient dissipative properties in order to allow an application of Gronwall's Lemma to the error term. As shown in [23], a uniform (in time) consistency estimate is sufficient to obtain convergence; however, the consistency estimate we proved is not uniform for small time, so we cannot directly employ the results in [23] to prove convergence in our case. Instead, we prove all the required estimates "from the scratch", then we use their exact quantitative form in order to conclude convergence. iv DEDICATION I would like to dedicate this work to My parents, my husband, my children, my siblings. v ACKNOWLEDGEMENTS First and foremost, I am most indebted to my advisor Dr. Adrian Tudorascu and my co-advisor Dr. Casian Pantea for their continued encouragement and support over these last few years. It has been a pleasure to work under their supervision. Without them, this dissertation could not have come about. Also, I would like to thank Dr.Pantea for providing me with financial support as a research assistant: Part I is joint work with Dr.

Background: Newborn infants have an increased sensitivity to pain and are more reactive to pain than older children and adults. Nurses play a crucial role in assessing pain, implementing and evaluating interventions to minimize neonatal pain using available resources especially nonpharmacologic techniques. Aim of the study: to develop and apply an educational program on pediatric nurses regarding selected nonpharmacologic techniques to relieve pain in neonates. Research design: Quasi-experimental research design was utilized in the present study. The study was carried out at Minia University for Obstetric and Pediatric and General Hospitals at neonatal care units. A convenient sample of 41 nurses was included in this study. Educational program for nurses' was done through using the following data collection tools 1) Pre-designed questionnaire sheet, 2) Observation checklists sheet and 3) Educational and training program. Results: It was revealed that there was an obvious increase in the total mean scores of knowledge and practice in post and follow up program phase compared with pretest phase, with a very highly significant difference (p<0.001). Conclusion: The education program had a significant impact on pediatric nurses' knowledge and practices regarding selected nonpharmacologic techniques to relieve pain in neonates. Recommendations: A continuous training and educational program should be planned and offered on regular basis for nurses regarding nonpharmacologic techniques to relieve pain in neonates.