Fractional Stefan Problem: A Survey of the Recent Results

被引:1
作者
Rogosin, S. [1 ]
Dubatovskaya, M. [1 ]
机构
[1] Belarusian State Univ, Minsk 220030, BELARUS
关键词
moving boundary problems; fractional derivatives and integrals; Stefan problems; phase changes; EQUATIONS;
D O I
10.1134/S1995080223080498
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The paper presents a survey of the recent fractional generalizations of the Stefan problem. This free boundary value problem in the classical setting deals with the diffusion of heat in a media accompanying with the change of phase state.
引用
收藏
页码:3535 / 3554
页数:20
相关论文
共 80 条
[1]   Continuity of the temperature in boundary heat control problems [J].
Athanasopoulos, I. ;
Caffarelli, L. A. .
ADVANCES IN MATHEMATICS, 2010, 224 (01) :293-315
[2]   The two-phase Stefan problem with anomalous diffusion [J].
Athanasopoulos, Ioannis ;
Caffarelli, Luis ;
Milakis, Emmanouil .
ADVANCES IN MATHEMATICS, 2022, 406
[3]  
Baleanu D., 2017, Series on Complexity, Nonlinearity and Chaos, V5
[4]   A Numerical Method for the Solution of the Two-Phase Fractional Lame-Clapeyron-Stefan Problem [J].
Blasik, Marek .
MATHEMATICS, 2020, 8 (12) :1-21
[5]   Numerical solution of the one phase 1D fractional Stefan problem using the front fixing method [J].
Blasik, Marek ;
Klimek, Malgorzata .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (15) :3214-3228
[6]   Realizable effective fractional viscoelasticity in heterogeneous materials [J].
Brenner, R. .
MECHANICS RESEARCH COMMUNICATIONS, 2019, 97 :22-25
[7]   A NOTE ON MODELS FOR ANOMALOUS PHASE-CHANGE PROCESSES [J].
Ceretani, Andrea N. .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2020, 23 (01) :167-182
[8]   On the Two-phase Fractional Stefan Problem [J].
del Teso, Felix ;
Endal, Jorgen ;
Luis Vazquez, Juan .
ADVANCED NONLINEAR STUDIES, 2020, 20 (02) :437-458
[9]   The one-phase fractional Stefan problem [J].
del Teso, Felix ;
Endal, Jorgen ;
Luis Vazquez, Juan .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2021, 31 (01) :83-131
[10]  
DELARUE F., 2022, Probab. Math. Phys., V3, P171, DOI DOI 10.2140/PMP.2022.3.171