  We investigate the escape behavior of systems governed by the one-dimensional
nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] +
D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a
double-well and $D, \nu$ are real parameters. For systems close to the steady
state we obtain an analytical expression of the mean first passage time,
yielding a generalization of Arrhenius law. Analytical predictions are in very
good agreement with numerical experiments performed through integration of the
associated Ito-Langevin equation. For $\nu\neq 1$ important anomalies are
detected in comparison to the standard Brownian case. These results are
compared to those obtained numerically for initial conditions far from the
steady state.
