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This note is concerned with the rigorous justification of the so-called hard congestion limit from a compressible system with singular pressure towards a mixed compressible-incompressible system modeling partially congested dynamics, for small data in the framework of BV solutions. We present a first convergence result for perturbations of a reference state represented by a single propagating large interface front, while the study of a more general framework where the reference state is constituted by multiple interface fronts is announced in the conclusion and will be the subject of a forthcoming paper. A key element of the proof is the use of a suitably weighted Glimm functional that allows to obtain precise estimates on the BV norm of the front-tracking approximation. Dans cette note, nous nous intéressons à la justification de la limite dite \"de congestion dure\" entre un système compressible avec pression singulière et un modèle limite mixte modélisant une dynamique partiellement congestionnée couplant zones compressibles et zones incompressibles. Cette limite est réalisée dans un cadre de solutions à données petites dans BV. Nous présentons un premier résultat de convergence pour des perturbations d'une solution de référence composée d'un unique front d'interface, l'étude de solutions de référence plus générales composées de fronts multiples fera quant à elle l'objet d'un article à venir. Un élément clé de la preuve est l'utilisation d'une fonctionnelle de Glimm adéquate permettant d'obtenir des estimations quantifiées sur la norme BV de la solution construite par l'approximation de suivi de fronts.

We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws, having small bounded variation, in one space dimension, must be functions of special bounded variation ( SBV ). For more than one equation, this SBV -regularity for non-degenerate fluxes is new also in the case of systems of conservation laws outside the context of genuine nonlinearity. For general smooth strictly hyperbolic systems of balance laws, this regularity fails, as known for systems of conservation laws: in such case we generalize the SBV -like regularity of the eigenvalue functions of the Jacobian matrix of the flux from conservation to balance laws. Proofs are based on extending Oleinink-type balance estimates, with the introduction of new source measure, a localization argument from [ 14 , 40 ], and observations in real analysis.

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation.

We consider the Cauchy problem for a strictly hyperbolic $2\\times 2$ system of conservation laws in one space dimension $u_t+[F(u)]_x=0, u(0,x)=\\bar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r_i(u), \\i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $\\lambda_i(u)$ the corresponding eigenvalue, then the set $\\{u: \\nabla \\lambda_i \\cdot r_i (u) = 0\\}$ is a smooth curve in the $u$-plane that is transversal to the vector field $r_i(u)$. Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature.For such systems we prove the existence of a closed domain $\\mathcal{D} \\subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S:\\mathcal{D} \\times [0,+\\infty)\\rightarrow \\mathcal{D}$ with the following properties. Each trajectory $t \\mapsto S_t \\bar u$ of $S$ is a weak solution of (1). Viceversa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t \\in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t,\\cdot) = S_t \\bar u. This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem with small initial data, for systems satysfying the above assumption.

To assess serum retinol and levels of carotenoids in children and adolescents with acquired immunodeficiency syndrome (AIDS) and to correlate low serum retinol and carotenoid levels with the presence of lipodystrophy, lipid profile changes, lipid peroxidation, and insulin resistance. A cross-sectional, controlled observational study was carried out with 30 children and adolescents with AIDS (mean age 9.1 y) receiving antiretroviral therapy (median length of treatment 28.4 mo), including 30 uninfected healthy controls matched for age and gender. Clinical and laboratory assessments were performed to determine nutritional status, presence of lipodystrophy, serum concentrations of retinol, β-carotene, lycopene, lipid profile (high-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triacylglycerols), lipid peroxidation (thiobarbituric acid-reactive substances), glycemia, and serum insulin (homeostasis model assessment for insulin resistance, cutoff point >3). Statistical analysis was done with chi-square test and Student's t test. Lipodystrophy was observed in 53.3% of patients with AIDS, and dyslipidemia was detected in 60% and 23% of subjects with human immunodeficiency virus and control subjects, respectively ( P = 0.004). A higher prevalence of retinol deficiency (60% versus 26.7%, P = 0.009) and β-carotene deficiency (23.3% versus 3.3%, P = 0.026) was found in the group with human immunodeficiency virus than in the control group. No correlation was found for low retinol and β-carotene levels, changes in lipid and glucose metabolism, or lipodystrophy in children and adolescents with AIDS. Despite the high frequency of dyslipidemia, lipodystrophy, and retinol and β-carotene deficiencies, it was not possible to demonstrate a correlation of these findings with lipid peroxidation and insulin resistance. More studies are needed to investigate the causes of retinol and β-carotene deficiencies in this population and the clinical consequences of these findings.

Background There is a gap in knowledge on the growth of children exclusively breastfed during the fifth and sixth months of life. This study aimed to assess the growth of infants who were exclusively breastfed for the first 6 months of life and compare the distributions of anthropometric measures based on the National Center for Health Statistics (NCHS, 1977) and World Health Organization (WHO, 2006) curves. Methods Cross-sectional study that measured the weight and length of 360 healthy and exclusively breastfed infants who were enrolled in a primary care program in Belem, Brazil from October 2006 to December 2008. The children were evenly grouped into age groups from 1 to 6 months of age. Results The mean weights were higher than the NCHS, 1977 mean weight for all of the studied groups regardless of gender and showed greater similarity to the WHO, 2006 mean weight, especially when standard deviations were considered. Regarding length, although the average length at birth was smaller, females had higher averages in the second and sixth months compared with the reference curves ( p  < 0.05). Conclusions Exclusive breastfeeding in the first 6 months of life provides adequate physical growth, resulting in height and weight gain curves that are similar to or greater than the NCHS, 1977 and WHO, 2006 curves. The greater mean weight at the fifth and sixth months of life suggests that the second-quarter growth curves of children who are exclusively breastfed are greater than those of children who receive other types of food.

While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperb These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. In addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. In all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.

Consider a general strictly hyperbolic, quasilinear system, in one space dimesion where , is a smooth matrix-valued map. Given an initial datum u (0, ·) with small total variation, let u ( t , ·) be the corresponding (unique) vanishing viscosity solution of (1) obtained as a limit of solutions to the viscous parabolic approximation u t  +  A ( u ) u x  =  μ u xx , as  μ → 0. For every T  ≥ 0, we prove the a-priori bound for an approximate solution of (1) constructed by the Glimm scheme, with mesh size , and with a suitable choice of the sampling sequence. This result provides for general hyperbolic systems the same type of error estimates valid for Glimm approximate solutions of hyperbolic systems of conservation laws u t  +  F ( u ) x = 0 satisfying the classical Lax or Liu assumptions on the eigenvalues λ k ( u ) and on the eigenvectors r k ( u ) of the Jacobian matrix A ( u ) =  DF ( u ). The estimate (2) is obtained introducing a new wave interaction functional with a cubic term that controls the nonlinear coupling of waves of the same family and at the same time decreases at interactions by a quantity that is of the same order of the product of the wave strength times the change in the wave speeds. This is precisely the type of errors arising in a wave tracing analysis of the Glimm scheme, which is crucial to control in order to achieve an accurate estimate of the convergence rate as (2).

The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.