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dc.contributor.authorGarra, R.
dc.contributor.authorFalcini, F.
dc.contributor.authorVoller, V.R.
dc.contributor.authorPagnini, G.
dc.description.abstractThe Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the square root of time. When memory or non-locality are introduced into the system however, this classic signal may be anomalous; replaced by a power-law advance with a time exponent that differs from n = 1/2. Up to now memory treatments in Stefan problem models have only been able to reproduce sub-diffusive front movements with exponents n < 1/2 and non-local treatments have only been able to reproduce super-diffusive behavior n > 1/2. In the present paper, using a generalized Caputo fractional derivative operator, we introduce new memory and non-local treatment for Stefan problems. On considering a limit case Stefan problem, related to the melting problem, we are able to show that, this gen- eral treatment can not only produce arbitrary power-law in time predictions for the front movement but, in the case of memory treatments, can also produce non-power-law anomalous behaviors. Further, also in the context of the limit problem, we are able to establish an equivalence between non-locality and a space varying conductivity and memory and a time varying conductivity.en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectStefan problemsen_US
dc.subjectfractional moving boundary problemsen_US
dc.subjectmelting processesen_US
dc.subjectanomalous diffusionen_US
dc.titleA generalized Stefan model accounting for system memory and non-localityen_US
dc.journal.titleInternational Communications in Heat and Mass Transferen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España