Pinning and de-pinning phenomena in front propagation in heterogeneous media
Nicolas Dirr, Nung Kwan Yip · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2006
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 when F 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 some semi-linear and reaction-diffusion equations.