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

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

The drug logistics process: an innovation experience

Purpose - The purpose of this paper is to present the latest innovations in the drug distribution processes of hospital companies, which are currently dealing with high inventory and storage costs and fragmented organizational responsibilities. Design/methodology/approach - The literature review and the in-depth analysis of a case study support the understanding of the unit dose drug distribution system and the subsequent definition of the practical implications for hospital companies. Findings - Starting from the insights offered by the case study, the analysis shows that the unit dose system allows hospitals to improve the patient care quality and reduce costs. Research limitations/implications - The limitations of the research are those related to the theoretical and exploratory nature of the study, but from a practical point of view, the work provides important indications to the management of healthcare companies, which have to innovate their drug distribution systems. Originality/value - This paper analyzes a new and highly topical issue and provides several insights for the competitive development of a fundamental sector

Uniqueness and Stability of Optimizers for a Membrane Problem

We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for general smooth bounded domains, and derive a symmetry result for radial ones. We strengthen our analysis by proving that, for this particular problem, there are no non-global local optima. When the membrane is made out of two materials, the problem reduces to a shape optimization problem. We lay the preliminary foundation for computable analysis of this type of problem by proving stability of solutions with respect to some of the parameters involved.Comment: 19 pages, 1 figur

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

A Metaphorical Language for Modelling

The workshop "Thinking in Practice" aimed to integrate both theoretical and practical methodologies. Therefore, we organizers decided to combine free discussions with more playful moments, along with some focused confrontations. These playful moments were intended to establish each workshop participant's position with respect to modelling, as well as to grasp and stress the most salient concepts emerging during the different sessions and discussions. This was in fact a purposeful methodological choice that allowed us to correlate the use of certain metaphors as models for the discussion, and as paths and guidelines for the various focus-exercises

The role of physiological traits in assortment among and within fish shoals

Individuals of gregarious species often group with conspecifics to which they are phenotypically similar. This among-group assortment has been studied for body size, sex and relatedness. However, the role of physiological traits has been largely overlooked. Here, we discuss mechanisms by which physiological traits—particularly those related to metabolism and locomotor performance—may result in phenotypic assortment not only among but also within animal groups. At the among-group level, varying combinations of passive assortment, active assortment, phenotypic plasticity and selective mortality may generate phenotypic differences among groups. Even within groups, however, individual variation in energy requirements, aerobic and anaerobic capacity, neurological lateralization and tolerance to environmental stressors are likely to produce differences in the spatial location of individuals or associations between group-mates with specific physiological phenotypes. Owing to the greater availability of empirical research, we focus on groups of fishes (i.e. shoals and schools). Increased knowledge of physiological mechanisms influencing among- and within-group assortment will enhance our understanding of fundamental concepts regarding optimal group size, predator avoidance, group cohesion, information transfer, life-history strategies and the evolutionary effects of group membership. In a broader perspective, predicting animal responses to environmental change will be impossible without a comprehensive understanding of the physiological basis of the formation and functioning of animal social groups. This article is part of the themed issue ‘Physiological determinants of social behaviour in animals’