1,720,962 research outputs found
Controllabilità e stabilità per equazioni di evoluzione degeneri di tipo Eulero-Bernoulli
No full textLa controllabilità e la stabilità delle equazioni differenziali alle derivate parziali governate da operatori lineari degeneri costituiscono un argomento importante sia dal punto di vista teorico sia dal punto di vista delle applicazioni. In particolare, questa tesi si concentra sulla controllabilità e sulla stabilità per equazioni delle travi unidimensionali di tipo Eulero-Bernoulli caratterizzate dalla presenza di operatori degeneri rispetto alla variabile spaziale.
Precisamente, i sistemi considerati possono essere visti come problemi di Cauchy astratti su opportuni spazi di Hilbert, le cui funzioni possiedono buone proprietà di integrabilità e soddisfano formule di Gauss-Green fondamentali. Pertanto, la buona positura di tali problemi può essere trattata nel contesto della teoria dei semigruppi di operatori e, quindi, si possono dimostrare risultati di esistenza così come di dissipatività dei sistemi. Inoltre, sia i risultati di controllabilità sia quelli di stabilità sono ottenuti mediante l'approccio energetico e il metodo dei moltiplicatori.
La tesi è divisa in cinque capitoli e la loro organizzazione segue un approccio semplice e diretto che conduce facilmente sia ai principali risultati ottenuti nel periodo del dottorato sia ad alcuni nuovi problemi aperti. Per rendere l'esposizione della tesi più agevole e indipendente, nel primo capitolo sono riportati tutti gli strumenti preliminari che saranno utilizzati nei capitoli successivi. Nel secondo capitolo sono riportati alcuni recenti sviluppi sulla controllabilità di equazioni degeneri delle travi quando il controllo è localizzato nel punto di bordo di non degenerazione. Queste equazioni sono considerate anche nel terzo capitolo, dove se ne studia la stabilità attraverso un termine di damping che agisce, anche in questo caso, sul punto di non degenerazione. Questi risultati sono poi utilizzati nel quarto capitolo, dove si dimostra la stabilità di equazioni degeneri non lineari delle travi. La tesi si conclude con il quinto capitolo, dove vengono sintetizzati alcuni problemi aperti già presentati nei capitoli precedenti.Controllability and stability of partial differential equations ruled by linear degenerate operators constitute an important topic in both theory and real world applications. In particular, this thesis focuses on the controllability and the stability for one-dimensional beam equations of Euler-Bernoulli type affected by leading degenerate operators with respect to the spatial variable.
Precisely, the systems under consideration can be viewed as abstract Cauchy problems on suitable Hilbert spaces, whose functions possess good integrability properties and satisfy fundamental Gauss-Green formulas. Therefore, the well-posedness of the problems can be treated in the framework of semigroup theory and, thus, existence results as well as dissipativeness of the systems can be achieved. Then, both the controllability and the stability results are obtained via the energy approach and the multiplier method.
The thesis is divided in five chapters and their organisation follows a simple and direct approach which quickly leads both to the main results pursued during the Ph.D. period and to some new open problems. In the first chapter we collect all the preliminary tools for the convenience of the reader and to make the exposition self-contained. The subject of the second chapter is represented by some recent developments in boundary control theory for linear degenerate beam equations. In the third chapter we show the exponential decay of the energy associated to some degenerate equations via a damping term acting on the boundary. In the fourth chapter we apply the results of the third chapter to prove the stability features for several classes of non-linear degenerate beam equations and some concrete applications are illustrated. Finally, the thesis concludes with the fifth chapter, where some open problems are presented
Degenerate fourth order parabolic equations with Neumann boundary conditions
No full textWe study the generation property for a fourth order operator in divergence or in non divergence form with suitable Neumann boundary conditions. As a consequence we obtain the well posedness for the parabolic equations governed by these operators. The novelty of this paper is that the operators depend on a function a : [0,1] → R+ that degenerates somewhere in the interval
Fourth-order differential operators with interior degeneracy and generalized Wentzell boundary conditions
Full text linkIn this article we consider the fourth-order operators A_1u:= (au′′ )′′ and A_2u:= au′′′′ in divergence and non divergence form, where a: [0, 1] → R+ degenerates in an interior point of the interval. Using the semigroup technique, under suitable assumptions on a, we study the genera-tion property of these operators associated to generalized Wentzell boundary conditions. We prove the well posedness of the corresponding parabolic problems
New results on controllability and stability for degenerate Euler-Bernoulli type equations
No full textIn this paper we study the controllability and the stability for a degenerate beam equation in divergence form via the energy method. The equation is clamped at the left end and controlled by applying a shearing force or a damping at the right end
Stability for some classes of degenerate nonlinear hyperbolic equations with time delay
Full text linkWe consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well-posedness and stability. Moreover, some illustrative examples are given
Boundary controllability for a degenerate beam equation
Full text linkThe paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control
acts on the right end of it. As a first step, we prove the existence of a solution for the homogeneous problem, then we prove some estimates on its energy. Thanks to them, we prove an observability inequality, and using the notion of solution by transposition, we prove that the initial problem is null controllable
A degenerate operator in non divergence form
Full text linkIn this paper we consider a fourth order operator in nondivergence form , where is a function that
degenerates somewhere in the interval. We prove that the operator generates an
analytic semigroup, under suitable assumptions on the function . We extend
these results to a general operator
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
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
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