We study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in N . In terms of the enthalpy h (x , t) , the evolution equation reads t h ( Δ) s Φ (h) = 0 , while the temperature is defined as u : = ...
phase transitionlong-range interactionsfree boundariesnonlinear and nonlocal equationfractional diffusionWe study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in N . In terms of the enthalpy h ( x , t ) , the ...
of a semi-infinite material through the one-phase fractional Lam\\\'e-Clapeyron-Stefan problem with an over-specified boundary condition on the fixed face $x=0$. The partial differential equation and one of the conditions on the free boundary include a time Caputo's fractional derivative of ...
https://www.youtube.com/watch?v=H5MEr9qzf-I Australian Geometric PDE Seminar Jack Thompson: On an overdetermined problem involving the fractional Laplacian Overdetermined problems are a type of boundary value problem where `too many' conditions are imposed on the solution. In general, such a ...
Section 5 contains the main original contribution of this article, which regards the two-phase fractional Stefan problem. First, we establish useful comparison properties between the one-phase and the two-phase problems. Later, we move to the study of a selfsimilar solution of particular interest...
Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order alpha a (0, 1) is taken in the Caputo sense. The first one has a constant condition on x = 0 and the second presents a flux condition T (x) (0,t) = q/t (alpha/2)....
The similarity method and explicit solutions for the fractional space one-phase Stefan problems In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space one-phase Stefan problem in terms of the three parametric Mittag-Leffer function E_{\\alpha,m;l}(z)...
One can debate the actual numbers, but the latest data from the Russian Ministry of Finance do in fact show a budget deficit of this magnitude by the end of 2023. I have chosen to implement the shock a bit faster than it really was, but that will, on the other hand, make up for ...
A variety of summary statistics have been proposed to describe the degree to which anisotropy is evident, one of the most common being fractional anisotropy (FA). FA tells the integrity of the fibres and ranged from 0 to 1 (Figure 3B). Nonetheless, one should aware of possible erroneous ...
(i.e., atypical) presentations of AD have gained better recognition in the last decade—while “progressive memory worsening” was one of the mandatory features of “probable AD” in the 1984 clinical criteria [26], this requirement was dropped in the 2011 revision of the diagnostic guidelines...