1,720,957 research outputs found
Qualitative Behavior of Solutions of a Chemotaxis System with Flux Limitation and Nonlinear Signal Production
No full textIn this paper we consider radially symmetric solutions of the following parabolic-elliptic cross-diffusion system {u(t)=Delta u-del(uf(|del v|(2))del v), 0=Delta v-mu(t)+g(u), mu(t)=1/|Omega|integral(Omega)g(u(& sdot;,t))dx u(x,0)=u(0)(x), in Omega x(0,infinity), with Omega a ball in R-N, N >= 1 under homogeneous Neumann boundary conditions, g(u) a regular function with the prototype g(u)=u(k), u >= 0, k>0. The function f(xi)=k(f) (1+xi)(-alpha), k (f )>0, describes gradient-dependent limitation of cross diffusion fluxes. Under suitable conditions on the data, we prove that the solution is global in time. If N >= 3, under conditions on f, g and initial data, we prove that if the solution u(x,t)blows up in L-infinity-norm at finite time T-max then for some p>1 it blows up also in L-p-norm. Moreover a lower bound of blow-up time is derived
Boundedness Through Nonlocal Dampening Effects in a Fully Parabolic Chemotaxis Model with Sub and Superquadratic Growth
Full text linkThis work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the mechanism of the two densities once their initial configurations are fixed in bounded impenetrable regions; in the specific, we establish that no gathering effect for the cells can appear in time provided that the dampening effect is strong enough. Mathematically, we are concerned with this problem {ut=Δu-χ∇·(u∇v)+auα-buα∫ΩuβinΩ×(0,Tmax),τvt=Δv-v+uinΩ×(0,Tmax),uν=vν=0on∂Ω×(0,Tmax),u(x,0)=u0(x)≥0,v(x,0)=v0(x)≥0,x∈Ω ̄,◊ for τ= 1 , n∈ N , χ, a, b> 0 and α, β≥ 1 . Herein u stands for the population density, v for the chemical signal and Tmax for the maximal time of existence of any nonnegative classical solution (u, v) to system (◊). We prove that despite any large-mass initial data u , whenever (The subquadratic case) 1≤α[removed]n+42-α,(The superquadratic case) β>n2and2≤α<1+2βn, actually Tmax= ∞ and u and v are uniformly bounded. This paper is in line with the result in Bian et al. (Nonlinear Anal 176:178–191, 2018), where the same conclusion is established for the simplified parabolic-elliptic version of model (◊), corresponding to τ= 0 ; more exactly, this work extends the study to the fully parabolic case Bian et al. (Nonlinear Anal 176:178–191, 2018
Blow-up phenomena in a parabolic–elliptic–elliptic attraction–repulsion chemotaxis system with superlinear logistic degradation
Full text linkThis paper is concerned with the attraction–repulsion chemotaxis system with superlinear logistic degradation, ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w)+λu−μuk,x∈Ω,t>0,0=Δv+αu−βv,x∈Ω,t>0,0=Δw+γu−δw,x∈Ω,t>0,under homogeneous Neumann boundary conditions, in a ball Ω⊂Rn (n≥3), with constant parameters λ∈R, k>1, μ,χ,ξ,α,β,γ,δ>0. Blow-up phenomena in the system have been well investigated in the case λ=μ=0, whereas the attraction–repulsion chemotaxis system with logistic degradation has been not studied. Under the condition that k>1 is close to 1, this paper ensures a solution which blows up in L∞-norm and Lσ-norm with some σ>1 for some nonnegative initial data. Moreover, a lower bound of blow-up time is derived
A nonlinear attraction-repulsion Keller–Segel model with double sublinear absorptions: criteria toward boundedness
Full text linkThis paper deals with the zero-flux attraction-repulsion chemo-taxis model
{u(t) = del center dot ((u + 1)(m1-1)del u-chi u(u + 1)(m2-1)del v in Omega x (0, T-max),
+xi u(u + 1)(m3-1)del w) + h(u)
(lozenge)
v(t) = Delta v - f (u)v in Omega x (0, T-max),
w(t) = Delta w - g(u)w in Omega x (0, T-max),
in the unknown (u, v, w)= (u(x, t), v(x, t), w(x, t)). Here, x is an element of Omega, a bounded and smooth domain of R-n(n >= 1), t, chi, xi > 0, m(1), m(2), m(3) is an element of R, and f (u), g(u) and h(u) sufficiently regular functions generalizing the prototypes f(u) = K(1)u(alpha), g(u) = K2u(gamma) and h(u) = ku - mu u(beta), with K-1, K-2, mu > 0, k is an element of R, beta > 1 and suitable alpha, gamma > 0. Besides, further regular initial data u(x, 0) = u(0)(x), v(x, 0) = v(0)(x), w(x, 0) = w(0)(x) >= 0 are given, whereas T-max is an element of (0, infinity] stands for the maximal instant of time up to which solutions to the system exist. We will derive relations between the parameters involved in (>) capable to warrant that u, v, w are global and uniformly bounded in time. The article generalizes and extends to the case of nonlinear effects and logistic perturbations some results recently developed in [3] where, for the linear counterpart and in the absence of logistics, criteria towards boundedness are established
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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