Pinning and de-pinning phenomena in front propagation in heterogeneous media

This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modelling of the propagation of phase boundaries in materials under the combined effects of an external driving force F and an underlying heterogeneous environment. The phenomenology is the existence of pinning states—stationary solutions—for small values of F, and the appearance of genuine motion whenF is above some threshold value. In the case of a periodic medium, we characterise quantitatively, near the transition regime, the scaling behaviour of the interface velocity as a function of F. The results are proved for a class of semilinear and reaction-diffusion equations.