scholarly journals On the Two-phase Fractional Stefan Problem

2020 ◽  
Vol 20 (2) ◽  
pp. 437-458 ◽  
Author(s):  
Félix del Teso ◽  
Jørgen Endal ◽  
Juan Luis Vázquez
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Free Boundary Problems ◽  
Classical Problem ◽  
Nonlocal Diffusion ◽  
Two Phase ◽  
Boundary Problems ◽  
Numerical Studies ◽  
The One ◽  
Evolution Type

AbstractThe classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

scholarly journals Lipschitz Regularity of Solutions to Two-phase Free Boundary Problems

2017 ◽  
Vol 2019 (7) ◽  
pp. 2204-2222 ◽  
Author(s):  
D De Silva ◽  
O Savin
Keyword(s):  
Free Boundary ◽  
Viscosity Solutions ◽  
Lipschitz Continuity ◽  
Free Boundary Problems ◽  
Linear Operators ◽  
Regularity Of Solutions ◽  
Two Phase ◽  
Boundary Problems ◽  
Lipschitz Regularity ◽  
Non Linear

AbstractWe prove Lipschitz continuity of viscosity solutions to a class of two-phase free boundary problems governed by fully non-linear operators.

scholarly journals On two phase free boundary problems governed by elliptic equations with distributed sources

2014 ◽  
Vol 7 (4) ◽  
pp. 673-693 ◽  
Author(s):  
Daniela De Silva ◽  
◽  
Fausto Ferrari ◽  
Sandro Salsa ◽  
◽  
...  
Keyword(s):  
Free Boundary ◽  
Elliptic Equations ◽  
Free Boundary Problems ◽  
Two Phase ◽  
Boundary Problems

scholarly journals A note on models for anomalous phase-change processes

2020 ◽  
Vol 23 (1) ◽  
pp. 167-182 ◽  
Author(s):  
Andrea N. Ceretani
Keyword(s):  
Phase Transitions ◽  
Energy Balance ◽  
Free Boundary ◽  
Phase Change ◽  
Stefan Problem ◽  
Fractional Derivatives ◽  
Free Boundary Problems ◽  
Natural Generalization ◽  
Change Processes ◽  
Boundary Problems

AbstractWe review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo’s definition. We survey the assumptions from which they are obtained and observe that the problems are nonequivalent though all of them reduce to a classical Stefan problem when the order of the fractional derivatives is replaced by one. We further show that a simple heuristic approach built upon a fractional version of the energy balance and the classical Fourier’s law leads to a natural generalization of the classical Stefan problem in which time derivatives are replaced by fractional ones.

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