1,721,147 research outputs found
Asymptotic profile for a two-terms time fractional diffusion problem
Full text linkWe consider the Cauchy-type problem associated to the time fractional partial differential equation:{partial derivative(t)u + partial derivative(beta)(t) u - Delta u = g(t, x), t > 0, x is an element of R-nu(0,x) = u(0)(x),with beta is an element of (0, 1), where the fractional derivative partial derivative(beta)(t) is in Caputo sense. We provide a sufficient condition on the right-hand term g(t, x) to obtain a solution in C-b ([0, infinity), H-s). We exploit a dissipative-smoothing effect which allows to describe the asymptotic profile of the solution in low space dimension
A structurally damped σ-evolution equation with nonlinear memory
No full textIn this paper, we investigate the global (in time) existence of small data solutions to the Cauchy problem for the following structurally damped σ-evolution model with nonlinear memory term: (Formula presented.) with σ>0. In particular, for γ∈((n−σ)/n,1), we find the sharp critical exponent, under the assumption of small data in L1. Dropping the L1 smallness assumption of initial data, we show how the critical exponent is consequently modified for the problem. In particular, we obtain a new interplay between the fractional order of integration 1−γ in the nonlinear memory term and the assumption that initial data are small in Lm, for some m>1
On the Shooting Method Applied to Richards’ Equation with a Forcing Term
No full textThe problem of modeling water flow in the root zone with plant root absorption is of crucial importance in many environmental and agricultural issues, and is still of interest in the applied mathematics community. In this work we propose a formal justification and a theoretical background of a recently introduced numerical approach, based on the shooting method, for integrating the unsaturated flow equation with a sink term accounting for the root water uptake model. Moreover, we provide various numerical simulations for this method, comparing the results with the numerical solutions obtained by MATLAB pdepe
Fujita modified exponent for scale invariant damped semilinear wave equations
Full text linkThe aim of this paper is to prove a blow-up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise decay order of the initial data. In addition, we give an upper bound estimate for the lifespan of the solution. It depends not only on the exponent of the nonlinear term and not only on the damping coefficient but also on the size of the decay rate of the initial data
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
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