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.
1
Mathematik in den Naturwissenschaften, Leipzig, Germany
2
Purdue University, West Lafayette, United States
N. Dirr; N.K. Yip. Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces and free boundaries, Tome 8 (2006) no. 1, pp. 79-109. doi: 10.4171/ifb/136
@article{10_4171_ifb_136,
author = {N. Dirr and N.K. Yip},
title = {Pinning and de-pinning phenomena in front propagation in heterogeneous media},
journal = {Interfaces and free boundaries},
pages = {79--109},
year = {2006},
volume = {8},
number = {1},
doi = {10.4171/ifb/136},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/136/}
}
TY - JOUR
AU - N. Dirr
AU - N.K. Yip
TI - Pinning and de-pinning phenomena in front propagation in heterogeneous media
JO - Interfaces and free boundaries
PY - 2006
SP - 79
EP - 109
VL - 8
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/136/
DO - 10.4171/ifb/136
ID - 10_4171_ifb_136
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%J Interfaces and free boundaries
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%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/136/
%R 10.4171/ifb/136
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