Mats Ehrnstrom, Joachim Escher, Bogdan-Vasile Matioc
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.
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http://arxiv.org/abs/1303.6724
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