Geodesic
Pinning of interfaces in a random medium with zero mean
Patrick W. Dondl1 ; Martin Jesenko2 ; Michael Scheutzow3
1Albert-Ludwigs-Universität Freiburg, Germany
2Univerza v Ljubljani, Slovenia
3Technische Universität Berlin, Germany
Interfaces and free boundaries, Tome 23 (2021) no. 3, pp. 305-321

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DOI

We consider two related models for the propagation of a curvature sensitive interface in a time independent random medium. In both cases we suppose that the medium contains obstacles that act on the propagation of the interface with an inhibitory or an acceleratory force. We show that the interface remains bounded for all times even when a small constant external driving force is applied. This phenomenon has already been known when only inhibitory obstacles are present. In this work we extend this result to the case of – for example – a random medium of random zero mean forcing.
DOI : 10.4171/ifb/455
Classification : 35-XX, 74-XX
Mots-clés : Quenched Edwards–Wilkinson model, phase boundaries, pinning, random environment, viscosity super-solutions

Patrick W. Dondl  1   ; Martin Jesenko  2   ; Michael Scheutzow  3

1 Albert-Ludwigs-Universität Freiburg, Germany
2 Univerza v Ljubljani, Slovenia
3 Technische Universität Berlin, Germany 
Patrick W. Dondl; Martin Jesenko; Michael Scheutzow. Pinning of interfaces in a random medium with zero mean. Interfaces and free boundaries, Tome 23 (2021) no. 3, pp. 305-321. doi: 10.4171/ifb/455
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     pages = {305--321},
     year = {2021},
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     doi = {10.4171/ifb/455},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/455/}
}
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