Methods and Applications of Analysis
Volume 20 (2013)
Steady-state fingering patterns for a periodic Muskat problem
Pages: 33 – 46
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.
Muskat problem, fingering patterns, existence, steady-state solutions, periodic solutions
2010 Mathematics Subject Classification
34A12, 34C23, 34C25, 70K42