Porous Medium Equation with A Drift: Free boundary Regularity
Analysis of PDEs
2021-08-12 v2
Abstract
We study regularity properties of the free boundary for solutions of the porous medium equation with the presence of drift. We show the regularity of the free boundary, when the solution is directionally monotone in space variable in a local neighborhood. The main challenge lies in establishing a local non-degeneracy estimate (Theorem 1.3 and Proposition 1.5), which appears new even for the zero drift case.
Cite
@article{arxiv.1812.08770,
title = {Porous Medium Equation with A Drift: Free boundary Regularity},
author = {Inwon Kim and Yuming Paul Zhang},
journal= {arXiv preprint arXiv:1812.08770},
year = {2021}
}
Comments
39 pages, 1 figure