1,721,006 research outputs found
Existence of Bounded Trajectories Via Upper and Lower Solutions
No full textThe paper deals with the boundary value problem (on the whole line) u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g is a continuous non-negative function with support [0, 1], and f is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for the problem when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u, u'). Applications of these results in the field of front-type solutions for reaction diffusion equations can be found in L. Malaguti, C. Marcelli, Math. Nachr. 242 (2002), 148—16
Heteroclinic solutions of boundary value problems on the real line involving general nonlinear differential operators
No full textWe discuss the solvability of the following strongly nonlinear
non-autonomous boundary-value problem:
(a(x(t))Φ(x (t)))' = f (t, x(t), x (t)) a.e. t ∈ R
x(−∞) = ν − , x(+∞) = ν + with ν − < ν + , where Φ : R → R is a general increasing homeomorphism, with Φ(0) = 0, a is a positive, continuous function and f is a Carathe ́dory nonlinear function. We provide some sufficient conditions for the solvability, which turn out to be optimal for a large class of problems. In particular, we highlight the role played by the behavior of f (t, x, ·) and Φ(·) as y → 0 related to that of f (·, x, y) as |t| →+∞.
We also show that the dependence on x, both of the differential operator
and of the right-hand side, does not influence in any way the existence
or non-existence of solutions
Wave fronts in reaction-diffusion equations
No full textA new approach, based on upper and lower solutions, was recently employed by the same authors to unify and generalize existing results for wave fronts in reaction-diffusion equations arising in combustion and genetic models. The statement of the problem and then main results are here explaned, and relations with existing results are analyzed. Some open problems and directions for futurre research are also indicated
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
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
Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations
No full textThis paper investigates the effects of a degenerate diffusion term in reaction-diffusion models ut=[D(u)ux]x + g(u) with Fisher-KPP type g. Both in the case when D(0) = 0 and when D(0) = D(l) = 0, with D(u) > 0 elsewhere, we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c* and we show the appearance of a sharp-type profile when c = c*. These results solve recent conjectures formulated by Sanchez-Garduno and Maini (J. Differential Equations 117 (1995) 281) and Satnoianu et al. (Discrete Continuous Dyn. Systems (Series B) 1 (2000) 339)
Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms
No full textThis paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction-diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c greater than or equal to c* and give an estimate for the threshold value c*. Our model takes into account both of a density dependent diffusion term and of a non-linear convection effect. Moreover, we do not require the main non-linearity g to be a regular C1 function; in particular we are able to treat both the case when g'(0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g'(0) = +∞. Our results generalize previous ones due to ARONSON and WEINBERGER [Adv. Math. 30 (1978), pp. 33 - 76], GIBBS and MURRAY (see MURRAY [Mathematical Biology, Springer-Verlag, Berlin, 1993]) and MCCABE, LEACH and NEEDHAM [SIAM J. Appl. Math. 59 (1998), pp. 870-899]. Finally, we obtain our conclusions by means of a comparison-type technique which was introduced and developed in this framework in a recent paper by the same authors
Finite speed of propagation in monostable degenerate reaction-diffusion-convection equations
No full textWe study the existence and properties of travelling wave solutions of the Fisher-KPP reaction-diffusion-convection equation u_t + h(u)u_x = [D(u)u_x]_x + g(u), where the diffusivity D(u) is simply or doubly degenerate. Both the cases when D(0) and D(1) are possibly zero real values or infinity, are treated. We discuss the effects, due to the presence of a convective term, concerning the property of finite speed of propagation. Moreover, in the doubly degenerate case we show the appearance of new types of profiles and provide their classification according to sharp relations between the nonlinear terms of the model. An application is also presented, concerning the evolution of a bacterial colony
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