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Pinning and De-Pinning Phenomena in Front Propagation in Heterogeneous Media
Nicolas Dirr and Aaron Nung Kwan Yip
This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modeling 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 characterize quantitatively, near the transition regime, the scaling behavior of the interface velocity as a function of F.
The results are proved for a class of some semi-linear and reaction-diffusion equations.