On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions

summary:We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as $t\rightarrow\infty$. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set

Asymptotic behavior for a nonlocal diffusion problem with Neumann boundary conditions and a reaction term

In this paper, we consider the following initial value problem u_t(x,t)=\int_{\Omega}J(x-y)(u(y,t)-u(x,t))dy-\gamma u^{p}(x,t)& \mbox{in}& \overline{\Omega}\times(0,\infty),u(x,0)=u_{0}(x)>0& \mbox{in}& \overline{\Omega},            where $\gamma\ in \{-1,1\}$ is a parameter, $\Omega$ is a bounded domain in      $\mathbb{R}^{N}$ with smooth boundary $\partial\Omega$, p>1, $J$:      $\mathbb{R}^N\longrightarrow\mathbb{R}$ is a kernel which is nonnegative,      measurable, symmetric, bounded and $\int_{\mathbb{R}^N}J(z)dz=1,$ the      initial datum $u_0 \ in C^0(\overline{\Omega})$, u_0(x)>0 in      $\overline{\Omega}$. We show that, if $\gamma=1$, then the solution $u$      of the above problem tends to zero as $t\rightarrow\infty$ uniformly in      $x\in\overline{\Omega}$, and a description of its asymptotic behavior is      given. We also prove that, if $\gamma=-1$, then the solution $u$ blows up      in a finite time, and its blow-up time goes to that of the solution of a      certain ODE as the $L^{\infty}$ norm of the initial datum goes to      infinity

Continuity of the quenching time in a semilinear heat equation with Neumann boundary condition

This paper concerns the study of a semilinear parabolic equation subject to Neumann boundary conditions and positive initial datum. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial datum. Finally, we give some numerical results to illustrate our analysis

Extinction time for some nonlinear heat equations

This paper concerns the study of the extinction time of the solution of the following initial-boundary value problem [left{% begin{array}{ll} hbox{$u_t=varepsilon Lu(x,t)-f(u)quad mbox{in}quad Omegatimesmathbb{R}_{+}$,} \ hbox{$u(x,t)=0quad mbox{on}quadpartialOmegatimesmathbb{R}_{+}$,} \ hbox{$u(x,0)=u_{0}(x)>0quad mbox{in}quad Omega$,} \ end{array}%right. ] where $Omega$ is a bounded domain in $mathbb{R}^{N}$ with smooth boundary $partialOmega$, $varepsilon$ is a positive parameter, $f(s)$ is a positive, increasing, concave function for positive values of s, $f(0)=0$, $int_{0}frac{ds}{f(s)}<+infty$, $L$ is an elliptic operator. We show that the solution of the above problem extincts in a finite time and its extinction time goes to that of the solution $alpha(t)$ of the following differential equation [alpha^{\u27}(t)=-f(alpha(t)),quad t>0,quad alpha(0)=M,] as $varepsilon$ goes to zero, where $M=sup_{xin Omega}u_{0}(x)$. We also extend the above result to other classes of nonlinear parabolic equations. Finally, we give some numerical results to illustrate our analysis

Prevalence of chronic kidney disease among people living with HIV/AIDS in Burundi: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Since little is known about chronic kidney disease (CKD) among people living with HIV/AIDS (PLWHA) in Sub-Saharan Africa, the prevalence and nature of CKD were assessed in Burundi through a multicenter cross-sectional study.</p> <p>Methods</p> <p>Patients underwent assessments at baseline and 3 months later. Glomerular Filtration Rate (GFR) was estimated using abbreviated 4-variable Modification of Diet in Renal Diseases (MDRD) and Cockroft-Gault estimation methods. Patients were classified at month 3 into various CKD stages using the National Kidney Foundation (NKF) definition, which combines GFR and urinary abnormalities. Risk factors for presence of proteinuria (PRO) and aseptic leukocyturia (LEU) were further analyzed using multiple logistic regression.</p> <p>Results</p> <p>Median age of the patients in the study (N = 300) was 40 years, 70.3% were female and 71.7% were on highly active antiretroviral therapy. Using the MDRD method, CKD prevalence in patients was 45.7%, 30.2% of whom being classified as stage 1 according to the NKF classification, 13.5% as stage 2 and 2% as stage 3. No patient was classified as stage 4 or 5. Among CKD patients with urinary abnormality, PRO accounted for 6.1% and LEU for 18.4%. Significant associations were found between LEU and non-steroidal anti-inflammatory drug (NSAID) use, previous history of tuberculosis, low body mass index and female gender and between PRO and high viral load.</p> <p>Conclusion</p> <p>Our study, using a very sensitive definition for CKD evaluation, suggests a potentially high prevalence of CKD among PLWHA in Burundi. Patients should be regularly monitored and preventative measures implemented, such as monitoring NSAID use and adjustment of drug dosages according to body weight. Urine dipsticks could be used as a screening tool to detect patients at risk of renal impairment.</p

The risk of thrombo-embolic events is increased in patients with germ-cell tumours and can be predicted by serum lactate dehydrogenase and body surface area

The aim of this study was to evaluate the risk of thrombo-embolic events (TEE) in patients with germ-cell tumours (GCT) who receive cisplatin-based chemotherapy, to compare this risk to that of a matched control group of non-GCT cancer patients, and to identify risk factors of TEE. The rate of TEE during the 6 months following the initiation of chemotherapy was assessed in 100 consecutive patients with GCT and in 100 controls with various neoplasms who were matched on sex and age, and who received first-line cisplatin-based chemotherapy during the same period of time at Institut Gustave Roussy, Villejuif, France. Data were subsequently tested on a validation group of 77 GCT patients treated in Lyon, France. A total of 19 patients (19%) (95% confidence interval (CI): 13–28) and six patients (6%) (95% CI: 3–13) had a TEE in the GCT group and the non-GCT control group, respectively (relative risk (RR): 3.4; P<0.01). Three patients from the GCT group died of pulmonary embolism. In multivariate analysis, two factors had independent predictive value for TEE: a high body surface area (>1.9 m2) (RR: 5 (1.8–13.9)) and an elevated serum lactate dehydrogenase (LDH) (RR: 6.4 (2.3–18.2)). Patients with no risk factor (n=26) and those with at least one risk factor (n=71) had a probability of having a TEE of 4% (95% CI: 1–19) and 26% (95% CI: 17–37), respectively. In the GCT validation set, 10 (13%) patients had a TEE; patients with no risk factor and those with at least one risk factor had a probability of having a TEE of 0 and 17% (95% CI: 10–29), respectively. Patients with GCT are at a higher risk for TEE than patients with non-GCT cancer while on cisplatin-based chemotherapy. This risk can be accurately predicted by serum LDH and body surface area. This predictive index may help to study prospectively the impact of thromboprophylaxis in GCT patients

Whole proteome analyses on Ruminiclostridium cellulolyticum show a modulation of the cellulolysis machinery in response to cellulosic materials with subtle differences in chemical and structural properties

Lignocellulosic materials from municipal solid waste emerge as attractive resources for anaerobic digestion biorefinery. To increase the knowledge required for establishing efficient bioprocesses, dynamics of batch fermentation by the cellulolytic bacterium Ruminiclostridium cellulolyticum were compared using three cellulosic materials, paper handkerchief, cotton discs and Whatman filter paper. Fermentation of paper handkerchief occurred the fastest and resulted in a specific metabolic profile: it resulted in the lowest acetate-to-lactate and acetate-to-ethanol ratios. By shotgun proteomic analyses of paper handkerchief and Whatman paper incubations, 151 proteins with significantly different levels were detected, including 20 of the 65 cellulosomal components, 8 non-cellulosomal CAZymes and 44 distinct extracytoplasmic proteins. Consistent with the specific metabolic profile observed, many enzymes from the central carbon catabolic pathways had higher levels in paper handkerchief incubations. Among the quantified CAZymes and cellulosomal components, 10 endoglucanases mainly from the GH9 families and 7 other cellulosomal subunits had lower levels in paper handkerchief incubations. An in-depth characterization of the materials used showed that the lower levels of endoglucanases in paper handkerchief incubations could hypothetically result from its lower crystallinity index (50%) and degree of polymerization (970). By contrast, the higher hemicellulose rate in paper handkerchief (13.87%) did not result in the enhanced expression of enzyme with xylanase as primary activity, including enzymes from the xyl-doc cluster. It suggests the absence, in this material, of molecular structures that specifically lead to xylanase induction. The integrated approach developed in this work shows that subtle differences among cellulosic materials regarding chemical and structural characteristics have significant effects on expressed bacterial functions, in particular the cellulolysis machinery, resulting in different metabolic patterns and degradation dynamics.This work was supported by a grant [R2DS 2010-08] from Conseil Regional d'Ile-de-France through DIM R2DS programs (http://www.r2ds-ile-de-france.com/). Irstea (www.irstea.fr/) contributed to the funding of a PhD grant for the first author. The funders provided support in the form of salaries for author [NB], funding for consumables and laboratory equipment, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. Omics Services provided support in the form of salaries for authors [VS, MD], but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors [NB, VS, MD] are articulated in the 'author contributions' section.info:eu-repo/semantics/publishedVersio

Status and Trends of Physical Activity Surveillance, Policy, and Research in 164 Countries: Findings From the Global Observatory for Physical Activity—GoPA! 2015 and 2020 Surveys

Background: Physical activity (PA) surveillance, policy, and research efforts need to be periodically appraised to gain insight into national and global capacities for PA promotion. The aim of this paper was to assess the status and trends in PA surveillance, policy, and research in 164 countries. Methods: We used data from the Global Observatory for Physical Activity (GoPA!) 2015 and 2020 surveys. Comprehensive searches were performed for each country to determine the level of development of their PA surveillance, policy, and research, and the findings were verified by the GoPA! Country Contacts. Trends were analyzed based on the data available for both survey years. Results: The global 5-year progress in all 3 indicators was modest, with most countries either improving or staying at the same level. PA surveillance, policy, and research improved or remained at a high level in 48.1%, 40.6%, and 42.1% of the countries, respectively. PA surveillance, policy, and research scores decreased or remained at a low level in 8.3%, 15.8%, and 28.6% of the countries, respectively. The highest capacity for PA promotion was found in Europe, the lowest in Africa and low- and lower-middle-income countries. Although a large percentage of the world’s population benefit from at least some PA policy, surveillance, and research efforts in their countries, 49.6 million people are without PA surveillance, 629.4 million people are without PA policy, and 108.7 million live in countries without any PA research output. A total of 6.3 billion people or 88.2% of the world’s population live in countries where PA promotion capacity should be significantly improved. Conclusion: Despite PA is essential for health, there are large inequalities between countries and world regions in their capacity to promote PA. Coordinated efforts are needed to reduce the inequalities and improve the global capacity for PA promotion