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 wit
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 : = ...
In this paper, we study a one-phase Stefan problem with time fractional diffusion equation, obtained from the standard diffusion equation by replacing the first order time-derivative by a fractional derivative of order α > 0 in the Caputo sense: C a Dαu(x, t) = λ2 ∂2u ∂x2 (...
A fractional Stefan’s problem with a boundary convective condition is solved, where the fractional derivative of orderα∈ (0, 1) is taken in the Caputo sense. Then an equivalence with other two fractional Stefan’s problems (the first one with a constant condition onx= 0 and the second ...
This model maps the motion of receptors within the membrane to the well-known Stefan problem; in fact, to the supercooled Stefan problem. The Stefan problem, introduced in the nineteenth century, applies to first-order phase transitions governed by the heat equation. The archetypal example is ...
The interested readers can refer to [35], [51] to find more information for the two phase-fluid dynamic. Authors of [11] investigated the numerical solution of the non–classical one–dimensional two–phase Stefan problem. Authors of [27] developed a new numerical procedure for solving Eq. ...
This makes it WTO-compliant and avoids the retaliation problem:no foreign government is going to retaliate against the U.S. for adopting a VAT, since it’s not targeting any one country’s products. How high would a VAT need to be to raise6.5% of GDPin revenue?
Based on this estimator, we propose a Bayesian change point detection method, which is one of the fastest Bayesian methodologies, and it is more robust to misspecification of the error terms than the competing methods. We demonstrate through empirical work the good performance of our approach vis...
Many claim the problem with fractional reserve banking is that it loans money into existence. It does, but under normal circumstances the money created by commercial banks disappears when loans are repaid or defaulted on, which therefore doesn’t create a permanent inflation of the money supply. ...
for the two-phase Navier–Stokes equations or Stefan problems, see the monograph [52]. Further applications of weighted function spaces include regularity issues for the Cahn-Hilliard equation [21], reaction-diffusion systems of Maxwell-Stefan type [29], Keller-Segel systems in critical spaces ...