Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type

By S. Eidelman, Anatoly N. Kochubei, S. Ivasyshen. 2004

237 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/60c0167a5926a61ad64850885daa8f1872c6d075

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Space-time fractional diffusion on bounded domains (2011, background): “1) was invented to properly handle initial values [9,10].”
Inverse problem for a three-parameter space-time fractional diffusion equation (2018, background): “This definition of the Caputo fractional derivative is intended to properly handle initial values [2, 6, 8], since its Laplace transform s q̃(s) − sq(0) incorporates the initial value in the same way the first derivative does.”
Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, background): “This construction was extended in [14,15,36,37], to equations with pseudo-differential operators, see also the reference list and an extensive overview in the monograph [16].”
A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2013, background): “This is intended to properly handle initial values [2, 3, 5], since its Laplace transform s f̃(s)−sβ−1f(0) incorporates the initial value in the same way the first derivative does.”
General Fractional Calculus, Evolution Equations, and Renewal Processes (2011, background): “2), the function uλ can be expressed via the Mittag-Leffler function Eα: uλ(t) = Eα(−λt); see [7, 13].”
Elliptic and parabolic equations for measures (2009, methodology): “On the one hand, the assumptions and techniques applied in this situation differ considerably from those used for obtaining Gaussian decay of densities in the case of bounded drifts or zero drifts (see [75], [143], [144], [77], [161], and also [8], where some assumptions on div b are used).”
Distributed order calculus and equations of ultraslow diffusion (2007, methodology): “1), but without subtracting t−αφ(0)), in the relaxation and diffusion problems, is caused by the fact that a solution of an equation with a Riemann–Liouville derivative typically has a singularity at the origin t = 0 (see, for example, [9]), so that the initial state of a system to be described by t”