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

Autor:	Roscani, Sabrina, Ryszewska, Katarzyna, Venturato, Lucas
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs 26A33 35R11 35R35 35R37
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.06690 Zobrazit plný text záznamu View this record from Arxiv