1,720,959 research outputs found
Global Existence and Uniqueness for Viscoelastic Equations With Nonstandard Growth Conditions
Get PDFThis paper is devoted to the study of generalized viscoelastic nonlinear equations with Dirichlet-Neumann boundary conditions. We establish the local and uniqueness of weak solutions results in Sobolev spaces with variable exponents. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space.
Mathematics Subject Classification (2010): 74D10, 74G25, 74G30, 40E10, 35B45.
Received 25 November 2021; Accepted 02 March 202
On the viscoelastic equation with Balakrishnan - Taylor damping and nonlinear boundary/interior sources with variable-exponent nonlinearities
Get PDFThis work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and nonlinear boundary interior sources with variable exponents. Under appropriate assumptions, we establish a uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.
Mathematics Subject Classification (2010): 49Q15, 35L05, 35L20 35B40, 35B35
Quasilinear parabolic equations with p(x)-Laplacian diffusion terms and nonlocal boundary conditions
Get PDFIn this study, we prove the existence of local solution for a quasi linear generalized parabolic equation with nonlocal boundary conditions for an elliptic operator involving the variable-exponent nonlinearities, using Faedo-Galerkin arguments and compactness method.
Mathematics Subject Classification (2010): 35K20, 35K59, 35B45, 35D30
Global nonexistence and blow-up results for a quasi-linear evolution equation with variable-exponent nonlinearities
Get PDFIn this paper, we consider a class of quasi-linear parabolic equations with variable exponents,
a (x, t) ut − ∆m(.)u = fp(.) (u)
in which fp(.) (u) the source term, a(x, t) > 0 is a nonnegative function, and the exponents of nonlinearity m(x), p(x) are given measurable functions. Under suitable conditions on the given data, a finite-time blow-up result of the solution is shown if the initial datum possesses suitable positive energy, and in this case, we precise estimate for the lifespan T ∗ of the solution. A blow-up of the solution with negative initial energy is also established.
Mathematics Subject Classification (2010): 35K92, 35B44, 35A01
Threshold results of blow-up solutions to Kirchhoff equations with variable sources
Get PDFThis paper analyzes an initial boundary value problem for variable source Kirchhoff-type parabolic equations. We aim to derive a new sub-critical energy threshold for finite-time blow-up, a new blow-up condition, and estimates for lifespan and upper bounds for blow-up time across various initial energy cases.
Mathematics Subject Classification (2010): 35B40, 35B44, 35K55
Received 17 February 2025; Accepted 01 June 2025
Upper bound estimate for the blow-up time of a class of integrodifferential equation of parabolic type involving variable source
Get PDFConsider a class of integrodifferential of parabolic equations involving variable source with Dirichlet boundary condition
\begin{equation*}
u_{t}=\Delta u-\int _{0}^{t}g\left(t-s\right) \Delta u\left(x,s\right) \mathrm{d} s+|u| ^{p(x) -2}u.
\end{equation*}
By means energy methods, we obtain a lower bound for blow-up time of the solution if blow-up occurs. Furthermore, assuming the initial energy is negative we establish a new blow-up criterion and give an upper bound for blow-up time of the solution
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
- …
