English

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.

Keywords

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}
}
R2 v1 2026-06-24T07:58:14.037Z