Abstract
In this paper we apply certain results in the theory of univalent functions to investigate the time evolution of the free boundary of a viscous fluid for a planar flow problem in the Hele–Shaw cell model under injection. To this end, we prove that the property of strongly Φ-likeness of order α∈(0,1] is preserved in time for both inner and outer problems, under the assumption of nonzero small surface tension.
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