1,720,965 research outputs found
Global boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with variable logistic source
No full textThis paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of variable logistic type u(t) = del . (phi(u)del u) - del. (phi(u)del upsilon) + g(x, u), -Delta upsilon = -upsilon + u, in (x, t) is an element of Omega x (0, T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Omega is a smooth and bounded domain in R-N(N >= 1) and g is an element of C-1 ((Omega) over bar x [0, infinity)) function satisfies g(x, s) 0 with g(x, 0) >= 0, x is an element of Omega and eta >= 0, mu > 0 are constants, k, m are measurable functions with 1 = sigma s(p) with p, q is an element of R, nu, chi, sigma > 0 when s >= 0. It is proved that if q = m(-) - 1 (critical case) and mu > chi (1 - 2/N (m(-) - p - 1)(+), then there exists a classical solution which is global in time and bounded. Moreover, if q is an element of (k(+) - 1, m(-) - 1), we obtain that there is a classical solution of the above system uniformly in time bounded without any restrictions on m(-) and mu. (c) 2022 Elsevier Inc. All rights reserved
Boundedness of solutions to a quasilinear parabolic-parabolic chemotaxis model with variable logistic source
No full textThis paper deals with the higher dimension quasilinear parabolic-parabolic chemotaxis model involving a source term of logistic type u(t) = del . (phi(u)del u) - V . (psi(u)del upsilon) + g(x, u), tau upsilon(t) = del upsilon - upsilon + u, in (x, t) is an element of Omega x (0, T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Omega is a smooth and bounded domain in R-N, N >= 1 and psi, phi, g are smooth, positive functions satisfying nu s(q) = sigma s(p), p,q is an element of R, nu, chi, sigma > 0 when s >= s(0) >1, g(x, s) 0, eta >= 0, mu > 0 constants and g(x, 0) >= 0, x is an element of Omega, where k, m are measurable functions with 0 1 which in logistic source term g(s) 0, eta >= 0 , > 0 as variable exponents k(.) >= 0, m(.) > 1 with k(+) mu(0) for some mu(0) > 0, then there exists a classical solution which is global in time and bounded. Furthermore, if q < m(-) - 1, we prove that the classical solutions to the above system are uniformly in-time-bounded without restriction on mu
Bornes sur le temps d’explosion pour une équation intégro-différentielle de type parabolique avec un terme réactif variable
No full textThis paper is concerned with the blow-up time of the solutions to an integro-differential problem of parabolic type with variable growth if blow-up occurs. By using the differential inequality technique, we obtain lower bounds for the blow-up time and some global existence results under some conditions to variable exponent of reaction, memory kernel, and initial value
Global attractors in a two-species chemotaxis system with two chemicals and variable logistic sources
No full textThis paper deals with the higher dimension quasilinear parabolic-parabolic chemotaxis model involving a source term of logistic type (formula presented), subject to the homogeneous Neumann boundary conditions in a ? ? RN (N ? 1) with smooth boundary. It is shown that for the attractionrepulsion case with ?2 ? 0, the global boundedness of solutions can be ensured by µ1, µ2 > 0 without any other assumptions, due to the contribution of the logistic sources included in addition to the repulsion mechanism. While for the attraction-attraction case with ?2 > 0, the global boundedness of solutions has to require logistic coefficients µ1, µ2 > 0 such that µ2 properly large. © 2024, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved
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
B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces
No full textIn this article, we consider the Laplace-Bessel differential operatorΔBk,n=∑i=1k∂2∂xi2+γixi∂∂xi+∑i=k+1n∂2∂xi2,γ1>0,…,γk>0.{\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0
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
DYNAMICS IN A PARABOLIC-ELLIPTIC CHEMOTAXIS SYSTEM WITH LOGISTIC SOURCE INVOLVING EXPONENTS DEPENDING ON THE SPATIAL VARIABLES
No full textWe consider the parabolic-elliptic chemotaxis system with the exponents depending on the spatial variables logistic source and nonlinear signal production: ut = Delta u-chi del (u del upsilon)+f (x, u), (x, t) is an element of Omega x (0, T), 0 = Delta upsilon - upsilon +u(gamma) in a bounded domain Omega subset of R-N (N > 1) with smooth boundary, subject to non negative initial data and homogeneous Neumann boundary conditions, where chi > 0, gamma >= 1 and partial derivative/partial derivative nu denotes the outward normal derivative on partial derivative Omega. The logistic function f fulfilling f (x, s) = 0, mu > 0 for all s > 0 with f (x, 0) >= 0 for all x is an element of Omega, where alpha : Omega -> [1, infinity) is a measurable function. It is proved that if 1 gamma or ess inf(x is an element of Omega) alpha (x) = gamma with mu > chi, then there exists a nonnegative classical solution (u, upsilon) that is global-in-time and bounded. In addition, under the particular conditions gamma = 1 and f (x, s) = mu (s - s(alpha(x)+1)), if mu is sufficiently large, the global bounded solution (u, upsilon) satisfies IIu (, t) - 1II(L)infinity(Omega) + II upsilon (, t) - 1II(L)infinity(Omega) 0 with k = min{ chi 2/4 , 1/2 } , C > 0. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameter conditions, which improves the known results
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