  The Polubarinova-Galin equation is derived from zero-surface-tension
Hele-Shaw flow driven by injection. In this paper, we classify degree three
polynomial solutions to the Polubarinova-Galin equation into three categories:
global solutions, solutions which can be continued after blow-up and solutions
which cannot be continued after blow-up. The coefficient region of the initial
functions in each category is obtained.
