On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions

In this paper we analyze the porous medium equation \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} %\begin{cases} u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad \textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm{on}\; \partial \Omega, t>0,\\ %u({\bf x},0)=u_0({\bf x})&{\bf x} \in \Omega,\\ %\end{cases} \end{equation} where $\Omega$ is a bounded and smooth domain of $\R^N$, with $N\geq 1$, and $I= [0,t^*)$ is the maximal interval of existence for $u$. The constants $a,b,c$ are positive, $m,p,q$ proper real numbers larger than 1 and the equation is complemented with nonlinear boundary conditions involving the outward normal derivative of $u$. Under some hypothesis on the data, including intrinsic relations between $m,p$ and $q$, and assuming that for some positive and sufficiently regular function u_0(\nx) the Initial Boundary Value Problem (IBVP) associated to \eqref{ProblemAbstract} possesses a positive classical solution u=u(\nx,t) on $\Omega \times I$: \begin{itemize} \item [$\triangleright$] when $p>q$ and in 2- and 3-dimensional domains, we determine a \textit{lower bound of} $t^*$ for those $u$ becoming unbounded in $L^{m(p-1)}(\Omega)$ at such $t^*$; \item [$\triangleright$] when $p<q$ and in $N$-dimensional settings, we establish a \textit{global existence criterion} for $u$. \end{itemize

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.We investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t*

The interplay between aerobic metabolism and antipredator performance: vigilance is related to recovery rate after exercise

When attacked by a predator, fish respond with a sudden fast-start motion away from the threat. Although this anaerobically-powered swimming necessitates a recovery phase which is fueled aerobically, little is known about links between escape performance and aerobic traits such as aerobic scope (AS) or recovery time after exhaustive exercise. Slower recovery ability or a reduced AS could make some individuals less likely to engage in a fast-start response or display reduced performance. Conversely, increased vigilance in some individuals could permit faster responses to an attack but also increase energy demand and prolong recovery after anaerobic exercise. We examined how AS and the ability to recover from anaerobic exercise relates to differences in fast-start escape performance in juvenile golden gray mullet at different acclimation temperatures. Individuals were acclimated to either 18, 22, or 26°C, then measured for standard and maximal metabolic rates and AS using intermittent flow respirometry. Anaerobic capacity and the time taken to recover after exercise were also assessed. Each fish was also filmed during a simulated attack to determine response latency, maximum speed and acceleration, and turning rate displayed during the escape response. Across temperatures, individuals with shorter response latencies during a simulated attack are those with the longest recovery time after exhaustive anaerobic exercise. Because a short response latency implies high preparedness to escape, these results highlight the trade-off between the increased vigilance and metabolic demand, which leads to longer recovery times in fast reactors. These results improve our understanding of the intrinsic physiological traits that generate inter-individual variability in escape ability, and emphasize that a full appreciation of trade-offs associated with predator avoidance and energy balance must include energetic costs associated with vigilance and recovery from anaerobic exercise

Variazione della prevalenza dell'infezione da H. pylori e ulcera peptica in pazienti dispeptici sardi

Background: Over the past 50 years the prevalence Helicobacter pylori infection has fallen as standards of living improved. The changes in the prevalence of infection and it manifestations (peptic ulcer disease and intestinal metaplasia) in a large cohort of Sardinians undergoing upper endoscopy for dyspepsia were investigated. Aim: To analyze the prevalence trend of H. pylori infection and peptic ulcer disease in patients that underwent upper endoscopy for dyspeptic symptoms during the period when the prevalence of H. pylori was rapidly falling. Methods: : A retrospective observational study was conducted involving patients undergoing endoscopy for dyspepsia from 1995 up to 2013. H. pylori status was assessed by histology, rapid urease test, and/or 13C-UBT. Gastric atrophy was assessed histologically. Data including non steroidal anti-inflammatory drugs (NSAIDs) use and the presence of peptic ulcers were collected. The prevalence of H. pylori was calculated for each quartile and for each birth cohort from 1910 to 2000. Results: 11,202 records were retrieved for the analysis (62.8% women). The overall prevalence of H. pylori infection was 43.8% (M: 46.6% vs. F: 42.0%; P = .0001). A dramatic decrease in prevalence infection occurred over the 19 year observation period. The birth cohort effect was evident in each category (quartile) reflecting the continuous decline in H. pylori acquisition. Over time the prevalence of ulcers also declined resulting in an increase in the proportion of H. pylori negative/NSAID positive and H. pylori negative/NSAID negative ulcers. The prevalence of atrophic changes also declined despite aging. Conclusions: The decline in H. pylori prevalence over time likely reflects the improvement in socioeconomic conditions in Sardinia such that H. pylori infection and its clinical outcomes including peptic ulcer is becoming less frequent even among dyspeptic patients

Riabitare la fabbrica: proposte di riciclaggio architettonico per il Distretto della Sedia

Associazione per lo Sviluppo del Distretto della Sedia (ASDI Sedia

Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions

We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and the reaction, we prove that, if the parameter is small enough, the problem admits at least four nontrivial solutions: two of such solutions are positive, one is negative, and one is sign-changing. Our approach is variational, based on critical point theory, Morse theory, and truncation techniques.Comment: 22 page