scholarly journals Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case

2019 ◽  
Vol 5 (2) ◽  
pp. 423-471 ◽  
Author(s):  
Dmitri Finkelshtein ◽  
Yuri Kondratiev ◽  
Pasha Tkachov
Keyword(s):  
Front Propagation ◽  
Nonlocal Diffusion ◽  
Multidimensional Case

Ogawa Integrability and a Condition for Convergence in the Multidimensional Case

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Nicolò Cangiotti ◽  
Sonia Mazzucchi
Keyword(s):  
Multidimensional Case

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.

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