  We introduce a notion of viscosity solutions for a nonlinear degenerate
diffusion equation with a drift potential. We show that our notion of solutions
coincide with the weak solutions defined via integration by parts. As an
application of the viscosity solutions theory, we show that the free boundary
uniformly converges to the equilibrium as time grows. In the case of a convex
potential, an exponential rate of free boundary convergence is obtained.
