Strongly Φ-like functions of order α in two-dimensional free boundary problems

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.