  We consider a zero-surface-tension two-dimensional Hele-Shaw flow in an
infinite wedge. There exists a self-similar interface evolution in this wedge,
an analogue of the famous Saffman-Taylor finger in a channel, exact shape of
which has been given by Kadanoff. One of the main features of this evolution is
its infinite time of existence and stability for the Hadamard ill-posed
problem. We derive several exact solutions existing infinitely by generalizing
and perturbing the one by Kadanoff.
