For a model for the propagation of a curvature sensitive interface in a time independent random medium, as well as for a linearized version which is commonly referred to as Quenched Edwards–Wilkinson equation, we prove existence of a stationary positive supersolution at non-vanishing applied load. This leads to the emergence of a hysteresis that does not vanish for slow loading, even though the local evolution law is viscous (in particular, the velocity of the interface in the model is linear in the driving force).
Nicolas Dirr
1
;
Patrick W. Dondl
2
;
Michael Scheutzow
3
1
University of Wales Cardiff, UK
2
Universität Freiburg, Germany
3
Technische Universität Berlin, Germany
Nicolas Dirr; Patrick W. Dondl; Michael Scheutzow. Pinning of interfaces in random media. Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 411-421. doi: 10.4171/ifb/265
@article{10_4171_ifb_265,
author = {Nicolas Dirr and Patrick W. Dondl and Michael Scheutzow},
title = {Pinning of interfaces in random media},
journal = {Interfaces and free boundaries},
pages = {411--421},
year = {2011},
volume = {13},
number = {3},
doi = {10.4171/ifb/265},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/265/}
}
TY - JOUR
AU - Nicolas Dirr
AU - Patrick W. Dondl
AU - Michael Scheutzow
TI - Pinning of interfaces in random media
JO - Interfaces and free boundaries
PY - 2011
SP - 411
EP - 421
VL - 13
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/265/
DO - 10.4171/ifb/265
ID - 10_4171_ifb_265
ER -
%0 Journal Article
%A Nicolas Dirr
%A Patrick W. Dondl
%A Michael Scheutzow
%T Pinning of interfaces in random media
%J Interfaces and free boundaries
%D 2011
%P 411-421
%V 13
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/265/
%R 10.4171/ifb/265
%F 10_4171_ifb_265
