Interfaces and Free Boundaries


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Volume 8, Issue 1, 2006, pp. 79–109
DOI: 10.4171/IFB/136

Published online: 2006-03-31

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

N. Dirr[1] and N.K. Yip[2]

(1) Mathematik in den Naturwissenschaften, Leipzig, Germany
(2) Purdue University, West Lafayette, United States

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.

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Dirr N., Yip N.K.: Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces Free Bound. 8 (2006), 79-109. doi: 10.4171/IFB/136