Steady-state fingering patterns for a periodic Muskat problem

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.