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

Changes in personal attitudes and perceived public opinions towards external childcare

This study investigates how the transition to parenthood relates to changes in personal attitudes and perceived public opinion towards external childcare for children under three. We use German panel data which capture cultural perceptions such as individual attitudes and perceived public opinions regarding day care for under threes. We analyze how both variables change during the family formation phase using panel regressions with linear between-within (hybrid) models. The findings suggest that cultural perceptions are strongly influenced by life course events. After their first child is born, parents are less skeptical of day care for under threes; however, we found no systematic changes in perceived public opinion. The results show an increasing gap between personal attitudes of parents and their perception of public opinion regarding childcare acceptance. These diverging views point to a conflict between the wish to use external childcare and societal expectations, which has strong implications for gender equality

Description of an operational tool for determining global solar radiation at ground using geostationary satellite images

International audienceAn operational tool for the fine-scale mapping of the incident solar radiation at ground is presented. This tool called "Heliosat station" makes use of image acquired in the visible spectral range by meteorological geostationary satellite to produce accurate maps of global radiation. Satellite data are directly received at ground by a cheap HF receiver and processed by a personal computer IBM-PC compatible using the already known Heliosat method. This method has been successfully tested during 30 consecutive months beginning January 1983. The first prototype of the Heliosat station was realized in 1985. Now a Heliosat station is routinely operated by Agence Française pour la Maîtrise de l'Energie since January 1987 for mapping solar radiation over Europe