Singularity Formation for the Stefan Problem

2018 ◽  
pp. 329-335
Author(s):  
J.J.L. Velázquez
Keyword(s):  
Stefan Problem ◽  
Singularity Formation

Singularity formation in the one-dimensional supercooled Stefan problem

1996 ◽  
Vol 7 (2) ◽  
pp. 119-150 ◽  
Author(s):  
Miguel A. Herrero ◽  
Juan J. L. Velázquez
Keyword(s):  
Stefan Problem ◽  
Finite Time ◽  
Blow Up ◽  
Half Line ◽  
Singularity Formation ◽  
Asymptotics Of Solutions ◽  
One Dimensional ◽  
The One

It is well-known that solutions to the one-dimensional supercooled Stefan problem (SSP) may exhibit blow-up in finite time. If we consider (SSP) in a half-line with zero flux conditions at t = 0, blow-up occurs if there exists T < ∞ such that limt↑Ts(t) > 0 and lim inft↑T⋅(t) = – ∞,s(t) being the interface of the problem under consideration. In this paper, we derive the asymptotics of solutions and interfaces near blow-up. We shall also use these results to discuss the possible continuation of solutions beyond blow-up.

ON STEFAN PROBLEM WITH PRESCRIBED CONVECTION

1994 ◽  
Vol 14 (2) ◽  
pp. 153-166
Author(s):  
Yi Fahuak ◽  
Qiu Yipin
Keyword(s):  
Stefan Problem

Stefan problem for a hyperbolic equation

2019 ◽  
Vol 2019 (4) ◽  
pp. 169-174
Author(s):  
M.T. Umirkhanov
Keyword(s):  
Hyperbolic Equation ◽  
Stefan Problem

Toward to usage of regularized Stefan problem solution in icing modeling

2020 ◽  
Author(s):  
Alexander V. Ivanov ◽  
Mikhail P. Levin ◽  
Tatiana V. Stenina ◽  
Sergey V. Strijhak
Keyword(s):  
Stefan Problem ◽  
Problem Solution

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 Modeling polymer crystallisation induced by a moving heat sink

Soft Matter ◽  
2021 ◽  
Author(s):  
Sabin Adhikari ◽  
Ahana Purushothaman ◽  
Alejandro A. Krauskopf ◽  
Christopher Durning ◽  
Sanat K. Kumar ◽  
...  
Keyword(s):  
Stefan Problem ◽  
Heat Sink ◽  
Polymer Melt

Recent experiments have shown that polymer crystallisation can be used to “move” and organize nanoparticles. As a first effort at modelling this situation we consider the classical Stefan problem modified for a polymer melt but driven by a heat sink.

scholarly journals Numerical solution of the Stefan problem

2021 ◽  
Vol 1809 (1) ◽  
pp. 012002
Author(s):  
N G Burago ◽  
A I Fedyushkin
Keyword(s):  
Numerical Solution ◽  
Stefan Problem
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