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

Sabrina Roscani; Katarzyna Ryszewska; Lucas Venturato

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arXiv · 2111.06690

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

Sabrina Roscani·Katarzyna Ryszewska·Lucas Venturato

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Abstract

Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys: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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Sabrina Roscani, Katarzyna Ryszewska, Lucas Venturato. 2021-11-12. A one-phase space -- fractional Stefan problem with no liquid initial domain. https://arxiv.org/abs/2111.06690

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