A one-phase space -- fractional Stefan problem with no liquid initial domain

2021/11/12 by Sabrina Roscani, Katarzyna Ryszewska, Roscani, Sabrina +3
Mathematics · #26A33 #35R11 #35R35 #35R37 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2111.06690

openalex publication_date 2021/11/12 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Taking into account the recent works \citeRoTaVe:2020 and \citeRys:2020, we consider a phase-change problem for a one dimensional material with a non-local flux, expressed in terms of the Caputo derivative, which derives in a space-fractional Stefan problem. We prove existence of a unique solution to a phase-change problem with the fractional Neumann boundary condition at the fixed face x=0, where the domain, at the initial time, consists of liquid and solid. Then we use this result to prove the existence of a limit solution to an analogous problem with solid initial domain, when it is not possible to transform the domain into a cylinder.

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