Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients

We study global in time existence versus blow-up in finite time of solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term posed in the one dimensional interval $(-R,R)$, $R>0$. Here the weight function is singular at the boundary of the domain $(-R,R)$, indeed it is such that $\rho(x)\sim (R-|x|)^{-q}$ as $|x|\to R$, with $q\ge0$. We show a different behavior of solutions depending on the three cases when $q>2$, $q=2$ and $q<2$.Comment: arXiv admin note: text overlap with arXiv:2007.12005, arXiv:1911.06043, arXiv:1911.0730

THE REDISCOVERY OF VISUAL AT THE BOLOGNA CHILDREN’S BOOK FAIR: THE SILENT BOOK CONTEST

The Bologna Children’s Book Fair (BCBF) is one of the capital events for the professionals in the field of children’s and young adults’ books and media contents, where a variegated and international audience meets to exchange ideas, projects, and creations. Moreover, during the years, the BCBF has established fruitful collaborations with many countries, Russia among them, where the international programme “The visual world of children’s books” was developed in collaboration with the Russian State Children’s Library of Moscow. As the very name of the programme suggests, both countries, Italy and Russia, have fully recognized the slow but steady rise of the iconic language, which is crucial for the construction of meaning in the newest and most appreciated children’s books. Another proof of the central role of images and visual storytelling was the founding of the Silent Book Contest (2014) for the best wordless visual narrative of the year, which was showing how images can be powerful cognitive attractors. This article will focus in particular on the last edition of the contest (2021), a virtual one due to the COVID-19 pandemic, during which the participants proposed works echoing the dramatic situation the world was (and is) living in. Now more than ever, ‘to look at’ seems to be synonymous with ‘to know’, as well as to ‘re-elaborate’

Uniqueness for fractional parabolic and elliptic equations with drift

We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.Comment: arXiv admin note: substantial text overlap with arXiv:1306.507

Blow-up and global existence for solutions to the porous medium equation with reaction and fast decaying density

We are concerned with nonnegative solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term $u^p$ with $p>1$. The density decays {\it fast} at infinity, in the sense that $\rho(x)\sim |x|^{-q}$ as $|x|\to +\infty$ with $q\ge 2.$ In the case when $q=2$, if $p$ is bigger than $m$, we show that, for large enough initial data, solutions blow-up in finite time and for small initial datum, solutions globally exist. On the other hand, in the case when $q>2$, we show that existence of global in time solutions always prevails. The case of {\it slowly} decaying density at infinity, i.e. $q\in [0,2)$, is examined in [41].Comment: arXiv admin note: substantial text overlap with arXiv:1911.0604

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

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 &gt; 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

Evaluación de proyecto de inversión de “Altos Emprendimientos S.A”

Trabajo final (Licenciatura en Economía con orientación en Empresas) -- Universidad Nacional de Córdoba. Facultad de Ciencias Económicas. Escuela de Graduados, 2024.Fil: Meglioli, Felipe. Universidad Nacional de Córdoba. Facultad de Ciencias Económicas; Argentina.En la presente investigación se aborda el análisis de factibilidad de un proyecto de loteo y construcción de unidades funcionales próximo al Lago Los Molinos, a cargo de Altos Emprendimientos S.A. El análisis se centró en determinar la viabilidad técnica del proyecto para determinar las dimensiones del terreno, los requisitos de proyecto, distribución y condiciones de uso del suelo junto con el personal requerido. Esta viabilidad implicó la determinación de la disposición del suelo para el uso de este por medio de la nivelación y parquización, como así también la determinación de las calles públicas para el tránsito. En relación con la elaboración de la viabilidad financiera, la misma se realizó desde la óptica de una evolución de las ventas de las unidades en función del tiempo estimado de la obra. En la viabilidad ambiental se plantearon diferentes estrategias para la incorporación de acciones tendientes a mitigar el impacto ambiental de la construcción en la zona. Por último, el análisis de viabilidad financiera permitió calcular el período de recupero actualizado, VAN y TIR del proyecto, nominado en dólares y con el cálculo de una tasa de descuento correspondiente. Los resultados del análisis en condiciones de certeza arrojaron la conveniencia de llevar a cabo el proyecto en términos del valor actual neto positivo obtenido y una tasa interna de retorno apenas superior a la tasa costo de oportunidad. Además, se realizó un análisis de riesgo con simulación de Montecarlo demostrando que ante variaciones del precio el proyecto continúa siendo rentable y un análisis de sensibilidad que demostró que en caso de un aumento del 21% de los costos el mismo dejaría de ser rentable.Fil: Meglioli, Felipe. Universidad Nacional de Córdoba. Facultad de Ciencias Económicas; Argentina