The shape of a free boundary driven by a line of fast diffusion
Analysis of PDEs
2020-04-01 v1
Abstract
We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free boundary is asymptotic to a line at infinity, whose angle to the horizontal is dicatated by the velocity of the wave imposed by the line. This helps understanding some rather counter-intuitive numerical simulations of [8].
Cite
@article{arxiv.2003.14005,
title = {The shape of a free boundary driven by a line of fast diffusion},
author = {Luis Caffarelli and Jean-Michel Roquejoffre},
journal= {arXiv preprint arXiv:2003.14005},
year = {2020}
}