1,720,965 research outputs found
A Liouville theorem for elliptic equations with a potential on infinite graphs
Full text linkBiagi S, Meglioli G, Punzo F. A Liouville theorem for elliptic equations with a potential on infinite graphs. Calculus of Variations and Partial Differential Equations . 2024;63(7): 165.We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is u equivalent to 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. We also show that on a special class of graphs the condition on the potential is optimal, in the sense that if it fails, then there exist infinitely many bounded solutions
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients
No full textMeglioli G. Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients . Discrete and Continuous Dynamical Systems. Series A. 2023.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 vari-able 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) (R - |x|)-q as |x|-+ R, with q > 0. We show a different behavior of solutions depending on the three cases when q > 2, q = 2 and q < 2
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Blow-up and global existence for solutions to the porous medium equation with reaction and fast decaying density
Full text linkWe are concerned with nonnegative solutions to the Cauchy problem for the porous medium equation with a variable density ρ(x) and a power-like reaction term up with p>1. The density decays fast at infinity, in the sense that ρ(x)∼|x|−q as |x|→+∞ with q≥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 slowly decaying density at infinity, i.e. q∈[0,2), is examined in Meglioli and Punzo (2020)
Nonlinear Parabolic Differential Equations: global existence and blow-up of solutions
Full text linkDOTTORATOL'argomento principale della tesi è lo studio dell'esistenza globale e del blow-up di soluzioni ad alcune equazioni differenziali paraboliche nonlineari. La tesi è suddivisa in tre parti in ciascuna delle quali si prende in considerazione una diversa equazione. Nella Parte I, viene analizzato un problema di Cauchy per una equazione dei mezzi porosi con densit'a variabile che dipende solo dallo spazio, e un termine di diffusione del tipo potenza: questa equazione rappresenta un modello matematico per l'evoluzione della temperatura del plasma. Utilizzando metodi di sotto- e soprasoluzioni, grazie anche al principio del confronto, si determina quando la soluzione del problema esiste globalmente in tempo e quando invece avviene blow-up in tempo finito. Nella seconda parte, Part II, si studia una classe di equazioni di reazione-diffusione definita su varietà Riemanniane complete, noncompatte e di volume infinito. Queste equazioni contengono nonlinearity di tipo potenza e una diffusione lenta del tipo mezzi porosi. Per il problema di Cauchy relativo a queste equazioni, si dimostra esistenza globale in tempo delle soluzioni per dati iniziali positivi e che siano appartenenti ad opportuni spazi . Inoltre, per queste soluzioni, si dimostra che esse sono limitate per tutti i tempi e si propone una stima quantitativa sulla loro norma . I metodi utilizzati per le dimostrazioni sono funzionali e si basano principalmente sulla validità delle disuguaglianze di Sobolev e Poincaré. Infine, nella Part III, si studia la nonesistenza di soluzioni per una classe di equazioni differenziali paraboliche quasilineari con un potenziale, definite in domini limitati. In particolare, si mostra come il comportamento del potenziale vicino alla frontiera del dominio e la nonlinearity di tipo potenza influenzano la nonesistenza delle soluzioni.The main topic of this thesis concerns the study of global existence and blow-up of solutions to certain nonlinear parabolic differential equations. The thesis is divided into three parts where three different equations are considered. In Part I, we analyze the Cauchy problem for the porous medium equation with a variable density, which depends on the space variable, and a power-like reaction term: this is a mathematical model of a thermal evolution of a heated plasma. Depending on the rate of decaying at infinity of the density function, by comparison method and suitable sub- and supersolutions, we determine whether the solution exists globally in time or blows up in finite time. In Part II, we consider reaction-diffusion equations posed on complete, noncompact, Riemannian manifolds of infinite volume. Such equations contain power-type nonlinearity and slow diffusion of the porous medium type. For the Cauchy problem related to this equation we prove global existence for positive initial data belonging to suitable spaces, and that solutions corresponding to such data are bounded at all positive times with a quantitative bound on their L norm. The methods of proof are functional analytic in character, as they depend solely on the validity of the Sobolev and the Poincar'{e} inequalities. In Part III, we are concerned with nonexistence results for a class of quasilinear parabolic differential equations with a potential in bounded domains. In particular, we investigate how the behavior of the potential near the boundary of the domain and the power nonlinearity affect the nonexistence of solutions.DIPARTIMENTO DI MATEMATICA34MARAZZINA, DANIELECORREGGI, MICHEL
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Comparison of model order reduction approaches in parametrized optimal control problems
No full textLAUREA MAGISTRALEI problemi di controllo ottimo parametrici sono una classe di problemi ampiamente studiata per via della loro versatile applicabilità in molti diversi casi. Può perciò rivelarsi utile, essere in grado di risolvere numericamente questo genere di problemi in modo efficiente. A tale proposito, in questo lavoro, indaghiamo due strategie di riduzione conosciute come: la riduzione gerarchica di modello (Hi-Mod) e il metodo delle basi ridotte (RB). Dapprima, studiamo separatamente la loro applicabilità a problemi di controllo ottimo parametrici arricchendo l'analisi con alcuni casi test. In particolare approfondiamo la buona posizione di un problema di controllo nella sua formulazione come problema di punto-sella, quando è stato ridotto attraverso la procedura Hi-Mod. In seguito, sperimentiamo una possibile combinazione delle due strategie citate e validiamo anche questa tecnica attraverso alcuni esempi numerici.Parametric optimal control problems are an important class of problems studied because of their adaptability to many real models in many different research areas. Hence, one could be interested in being able to numerically solve this kind of problems efficiently. To this aim, this work wants to investigate two different reduction strategies known as: the hierarchical model reduction method (Hi-Mod) and the reduced basis method (RB). First of all, we separately study their applicability to parametrized optimal control problems and we also present some numerical test cases. In particular, we analyze the well-posedness of the saddle-point formulation of an optimal control problem that has been hierarchically reduced. Then, we propose a possible way to combine the two methods mentioned above. We validate this procedure thanks to some numerical examples
On the uniqueness for the heat equation with density on infinite graphs
No full textMeglioli G. On the uniqueness for the heat equation with density on infinite graphs. Journal of Differential Equations. 2025;425:728-762.We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of possibly vanishing density, showing that these two scenarios lead to two different classes of uniqueness
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