  The mathematical modeling of tumor growth leads to singular stiff pressure
law limits for porous medium equations with a source term. Such asymptotic
problems give rise to free boundaries, which, in the absence of active motion,
are generalized Hele-Shaw flows. In this note we use viscosity solutions
methods to study limits for porous medium-type equations with active motion. We
prove the uniform convergence of the density under fairly general assumptions
on the initial data, thus improving existing results. We also obtain some
additional information/regularity about the propagating interfaces, which, in
view of the discontinuities, can nucleate and, thus, change topological type.
The main tool is the construction of local, smooth, radial solutions which
serve as barriers for the existence and uniqueness results as well as to
quantify the speed of propagation of the free boundary propagation.
