Escape time in anomalous diffusive media

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation ${\partial }_t\rho ={\partial }_x\left[{\partial }_{x}U\rho \right]+D{\partial }_x^2{\rho }^{\nu },$ where the potential of the drift, $U\left(x\right),$ 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 $\nu \ne 1,$ 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.