Duration of transient fronts in a bistable reaction-diffusion equation in a one-dimensional bounded domain

The duration of transient fronts in a bistable reaction-diffusion equation in a bounded domain is considered. The speed of the front decreases exponentially with the length of the domain, and the duration increases exponentially with the domain length. The duration of the fronts generated from random initial conditions is distributed in a power-law form up to a cutoff time. The cutoff time then increases exponentially with the domain length so that the power-law distribution dominates for large domains. Further, external noise of intermediate strength increases the mean duration of the fronts. The increases in the duration with the domain length become almost linear, however, in the presence of asymmetry in the cubic nonlinearity.