On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Blow-up versus global existence of solutions for reaction-diffusion equations on classes of Riemannian manifolds

It is well known from the work of Bandle et al. (J Differ Equ 251:2143-2163, 2011) that the Fujita phenomenon for reaction-diffusion evolution equations with power nonlinearities does not occur on the hyperbolic space H-N, thus marking a striking difference with the Euclidean situation. We show that, on classes of manifolds in which the bottom lambda of the L-2 spectrum of -delta is strictly positive (the hyperbolic space being thus included), a different version of the Fujita phenomenon occurs for other kinds of nonlinearities, in which the role of the critical Fujita exponent in the Euclidean case is taken by lambda. Such nonlinearities are time-independent, in contrast to the ones studied in Bandle et al. (2011). As a consequence of our results we show that, on a class of manifolds much larger than the case M = H-N considered in Bandle et al. (2011), solutions to (1.1) with power nonlinearity f(u) = u(p), p > 1, and corresponding to sufficiently small data, are global in time. Though qualitative similarities with similar problems in bounded, Euclidean domains can be seen in the results, the methods are significantly different because of noncompact setting dealt with

Global existence for reaction-diffusion evolution equations driven by the p-Laplacian on manifolds

We consider reaction-diffusion equations driven by the p-Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have L2 spectrum bounded away from zero, the main example we have in mind being the hyperbolic space of any dimension. It is shown that, under appropriate conditions on the parameters involved and smallness conditions on the initial data, global in time solutions exist and suitable smoothing effects, namely explicit bounds on the L∞ norm of solutions at all positive times, in terms of Lq norms of the data. The geometric setting discussed here requires significant modifications w.r.t. the Euclidean strategies

How environmental sustainability labels affect food choices: Assessing consumer preferences in southern Italy

This paper assesses consumer preferences and willingness to pay for three different environmental sustainability labels (EU Organic Farming, Rainforest Alliance, ‘Per il Clima-Legambiente’) and information cues about the origin displayed on a processed food product, namely tomato puree. Using a choice experiment and conditional logit models, the results show that: i) preferences for the environmental sustainability labelled product increase when consumers have proper knowledge about the meaning of the labels; ii) the information cue about the product’s domestic origin is important for all consumers, regardless of their education, unlike environmental sustainability labels that are more appreciated by well-educated consumers; iii) consumers’ willingness to pay is higher for labels with greater market penetration, regardless of certification by private or public organisations. Findings suggest that the adoption of environmental sustainability labels by food producers should be combined with effective information policies aimed at increasing consumer awareness

Measuring the effect of formal education on income inequality: A longitudinal analysis across Mediterranean countries

The paper aims at investigating the role of gender and personal education in explaining differences in generating individual earnings and their effects on income inequality. The analysis involves four countries of Southern Europe (Greece, Italy, Portugal, and Spain) in light of the macroeconomic and institutional settings and policy frameworks. Once that the main determinants of income have been sketched through random effects models, the ANOGI (Analysis of Gini) decomposition is performed in order to evaluate the contribution of each subgroup of population with different formal education to the overall income inequality and to assess the degree to which each subpopulation is stratified. In short, Greece and Portugal show the largest gender earnings gaps and the largest differences in returns on education, while earnings inequality is more severe for Italian and Portuguese women. In each country, except for Italy, lower educated workers show the lowest amount of overlapping and, therefore, high levels of income stratification, while higher educated individuals are usually less stratified. Italy instead shows similar degrees of overlapping for both the lowest and the highest education levels

Understanding pro-environmental travel behaviours in Western Europe

This study aims at understanding, from a gender perspective, the reasons behind citizens’ choice of using public transport, and whether this choice is driven by pro-environmental behaviour. Using Eurobarometer data (2013), we perform ordered logistic regressions comparatively for Germany, Italy and the Netherlands. Financial, political and environmental factors are shown to have significant roles in shaping travel behaviours, with interesting gender and cross-country differences

The determinants of land use in Italy from a spatial perspective: A re-interpretation at the time of Covid-19

Since the post-Second World War period, territorial development in Italy has been characterised by unsustainable settlement patterns, including the unplanned and wildfire growth of urban systems and the propensity to overbuilding. Systematic knowledge of the key aspects of land use patterns is the basis for planning sustainable land development. Furthermore, the outbreak of the COVID-19 pandemic has accentuated the need to re-address land management to ensure public safety and protection. By using the Spatial Durbin Model (SDM), this work aims to: i) analyse the determinants that best quantitatively describe land use patterns in Italian municipalities; ii) provide a re-interpretation of the main results in light of the territorial re-planned process required by the Covid-19 pandemic. The results suggest that monitoring land use and strengthening quality and cooperation between local institutions are needed to preserve the environment and ecosystem services that underlie more sustainable land use planning

Network communities of dynamical influence

Fuelled by a desire for greater connectivity, networked systems now pervade our society at an unprecedented level that will affect it in ways we do not yet understand. In contrast, nature has already developed efficient networks that can instigate rapid response and consensus when key elements are stimulated. We present a technique for identifying these key elements by investigating the relationships between a system’s most dominant eigenvectors. This approach reveals the most effective vertices for leading a network to rapid consensus when stimulated, as well as the communities that form under their dynamical influence. In applying this technique, the effectiveness of starling flocks was found to be due, in part, to the low outdegree of every bird, where increasing the number of outgoing connections can produce a less responsive flock. A larger outdegree also affects the location of the birds with the most influence, where these influentially connected birds become more centrally located and in a poorer position to observe a predator and, hence, instigate an evasion manoeuvre. Finally, the technique was found to be effective in large voxel-wise brain connectomes where subjects can be identified from their influential communities

Exploring antecedents of innovations for small- and medium-sized enterprises' environmental sustainability: An interpretative framework

The need to pursue sustainable development has become a central topic in Western countries due to citizens' greater sensitivity to improving environmental and social conditions. Companies can reach this objective more easily through green innovations, which are now considered a strategic opportunity that simultaneously allows for adherence to sustainable development criteria and the pursuit of competitive advantages. Scholars have identified the determinants that encourage companies to adopt green innovations, but the outcomes of their investigations thus far have often been ambiguous and contradictory. Our paper proposes an interpretative framework for addressing such inconsistencies. Using the partial least squares structural equation modelling (PLS-SEM) methodology, we validate this framework on a sample of small- and medium-sized enterprises (SMEs) and show that SMEs' choices are influenced by cultural elements and stimulated by the prospect of obtaining economic advantages over competitors. SMEs also pay close attention to stakeholder solicitations, while public administration does not affect their eco-innovating choices. The results have policy implications for executives and insiders

Sustainable urban mobility: evidence from three developed European countries

The importance acquired by private cars as the leading travel mode in most advanced countries has drawn attention to concerns related to pro-environmental travel behaviour. Indeed, the car has brought great benefits to society, albeit causing a whole lot of environmental and socio-economic consequences. In this perspective, we exploit Eurobarometer data on the attitudes of Europeans towards urban mobility to investigate the main motivations of citizens’ public transport use frequency. Ordered logistic regressions are estimated by country (Germany, Italy, and the Netherlands) and by gender. Our results suggest the key role played by a comprehensive set of socio-demographic, economic, and environmental aspects in determining urban travel behaviour. Moreover, our investigation brings to light some relevant cross-country and cross-gender commonalities and differences. The provided evidence may give policymakers a better knowledge of travel behaviour, useful for designing new interventions for environmentally-sustainable travelling