The Two-Phase Stefan Problem with Anomalous Diffusion
Analysis of PDEs
2021-12-01 v1
Abstract
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan problem to be part of the General Filtration Problems; a class which includes the Porous Medium Equation. In this work, we prove that the weak solutions to both Stefan and Porous Media problems are continuous.
Cite
@article{arxiv.2111.15600,
title = {The Two-Phase Stefan Problem with Anomalous Diffusion},
author = {Ioannis Athanasopoulos and Luis Caffarelli and Emmanouil Milakis},
journal= {arXiv preprint arXiv:2111.15600},
year = {2021}
}