87,042 research outputs found
A Short Presentation of Emmanuele’s Work
No full textAs the title suggests, this is a short presentation of DiBenedetto’s mathematical work. In the first part Ugo Gianazza gives a general overview, without entering too much into details of specific papers; in his contribution Daniele Andreucci focuses on DiBenedetto’s accomplishments in BioMathematics
Universal Bounds at the Blow-Up Time for Nonlinear Parabolic Equations
No full textWe prove a priori supremum bounds for solutions to doubly degenerate nonlinear parabolic equations, with a forcing term f(x)u^p where u is the solution, p> 1, f is strongly dependent on the space variable x, as t approaches the time when u becomes unbounded. Such bounds are universal in the sense that they do not depend on u. Here f may become unbounded, or vanish, as x goes to 0. When f =1, we also prove a bound below, as well as uniform localization of the support, for subsolutions to the corresponding Cauchy problem
The cauchy-dirichlet problem for the porous media equation in cone-like domains
No full textWe investigate the behavior for large times of nonnegative solutions to the Dirichlet problem in cone-like domains for the porous media equation. We obtain optimal estimates for the sup norm of the solution and for the size of its support. We also consider the case where a damping term depending on the space gradient of the solution appears. In this case we also identify the critical behavior of the damping term discriminating between decay to zero of a suitable moment of the solution as t → + ∞, and stabilization of the moment to a positive constant. © 2014 Society for Industrial and Applied Mathematics
“Types and components of urban blue spaces that have a positive impact on mental health and well-being: a systematic review”
No full text“EKLIPSE Mental Health and Green and Blue open spaces" è un progetto sul tema della valutazione dell’impatto sulla salute mentale e il benessere delle persone degli spazi aperti urbani “verdi e blu”, anche mediante l’individuazione di criteri e indicatori prestazionali nel confronto con le sfide poste alla salute dal cambiamento climatico (ricerca in corso). EKLIPSE è un progetto Horizon 2020 finanziato dall'Unione europea che punta a migliorare l'interfaccia tra scienza, politica e società. I gruppi di lavoro di esperti istituiti da EKLIPSE svolgono attività di ricerca rivolta a soddisfare le richieste di conoscenze da parte dei responsabili politici. Il gruppo di lavoro coordinato da Maria Beatrice Andreucci con Annamaria Lammel (Université Paris 8) e Sjerp de Vries (Wageningen University and Research) sta lavorando dal 2017 a una richiesta presentata dal gruppo di lavoro Biodiversity & Health del 3rd French Plan on Health and Environment (PNSE3) – del Ministero dell’Ambiente francese (MTES) in cofinanziamento con l’Organizzazione Mondiale della Sanità. Tale approccio è stato identificato per promuovere l’utilizzo delle NBS nei progetti finanziati nell’ambito di H2020, con l’obiettivo di incrementare la resilienza umana al cambiamento climatico, costruendo una base di evidenza scientifica in termini di benefici prodotti dagli spazi aperti
Socialism: Historical Aspects
No full textInternational Encyclopedia of the Social and Behavioral Science
Optimal decay rate for degenerate parabolic equations on noncompact manifolds
No full textWe consider an initial value problem for a doubly degenerate
parabolic equation in a noncompact Riemannian manifold. The
geometrical features of the manifold are coded in either a
Faber-Krahn inequality or a relative Faber-Krahn inequality. We
prove optimal decay and space-time local estimates of solutions. We
employ a simplified version of the by now classical local approach
by DeGiorgi, Ladyzhenskaya-Uraltseva, DiBenedetto which is of
independent interest even in the euclidean case
Asymptotic Estimates for the p-Laplacian on Infinite Graphs with Decaying Initial Data
No full textWe consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for nonnegative solutions, when the initial data has finite mass, and also sharp evaluation for the confinement of mass, i.e., the effective speed of propagation. We provide estimates for some moments of the solution, defined using the distance from a given vertex. Our technique relies on suitable inequalities of Faber-Krahn type, and looks at the local theory of continuous nonlinear partial differential equations. As it is known, however, not all of this approach can have a direct counterpart in graphs. A basic tool here is a result connecting the supremum of the solution at a given positive time with the measure of its level sets at previous times. We also consider the case of slowly decaying initial data, where the total mass is infinite
Asymptotic properties of solutions to the Cauchy problem for degenerate parabolic equations with inhomogeneous density on manifolds
No full textWe consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending on the behavior of the density function at infinity and the geometry of the manifold, which is described in terms of its isoperimetric function. We establish for the solutions properties as: stabilization of the solution to zero for large times, finite speed of propagation, universal bounds of the solution, blow up of the interface. Each one of these behaviors of course takes place in a suitable range of parameters, whose definition involves a universal geometrical characteristic function, depending both on the geometry of the manifold and on the asymptotics of the density at infinity
Large time behavior for the porous medium equation with convection
No full textWe consider the Cauchy problem for the porous medium
equation with nonlinear convection, when the nonlinearities are the
same in the convection and in the diffusion terms. We get a new
sharp bound of the solution for large times
Large time behaviour for degenerate parabolic equations with convection
No full textWe consider the Cauchy problem for a doubly nonlinear parabolic equation, obtaining optimal estimates both for the sup norm of nonnegative solutions, and for their support for large times
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