A New Mathematical Formulation for a Phase Change Problem with a Memory Flux
Analysis of PDEs
2018-10-18 v2 Mathematical Physics
math.MP
Abstract
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered. The model obtained involves fractional derivatives with respect on time in the sense of Caputo and in the sense of Riemann--Liouville. An integral relationship for the free boundary which is equivalent to the `fractional Stefan condition' is also obtained.
Cite
@article{arxiv.1805.09115,
title = {A New Mathematical Formulation for a Phase Change Problem with a Memory Flux},
author = {Sabrina Roscani and Julieta Bollati and Domingo Tarzia},
journal= {arXiv preprint arXiv:1805.09115},
year = {2018}
}
Comments
26 pages, 2 figures