Steady-state fingering patterns for a periodic Muskat problem
Analysis of PDEs
2013-03-28 v1 Mathematical Physics
math.MP
Abstract
We study global bifurcation branches consisting of stationary solutions of the Muskat problem. It is proved that the steady-state fingering patterns blow up as the surface tension increases: we find a threshold value for the cell height with the property that below this value the fingers will touch the boundaries of the cell when the surface tension approaches a finite value from below; otherwise, the maximal slope of the fingers tends to infinity.
Cite
@article{arxiv.1303.6724,
title = {Steady-state fingering patterns for a periodic Muskat problem},
author = {Mats Ehrnstrom and Joachim Escher and Bogdan-Vasile Matioc},
journal= {arXiv preprint arXiv:1303.6724},
year = {2013}
}