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MiS Preprint

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.

MSC Codes:
35B27, 35B40, 35K55, 35K57
reaction-diffusion, pinning, propagation failure, pulsating waves

Related publications

2006 Repository Open Access
Nicolas Dirr and Aaron Nung Kwan Yip

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

In: Interfaces and free boundaries, 8 (2006) 1, pp. 79-109