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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
50/2005

Pinning and De-Pinning Phenomena in Front Propagation in Heterogeneous Media

Nicolas Dirr and Aaron Nung Kwan Yip

Abstract

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.

Received:
May 13, 2005
Published:
May 13, 2005
MSC Codes:
35B27, 35B40, 35K55, 35K57
Keywords:
reaction-diffusion, pinning, propagation failure, pulsating waves

Related publications

inJournal
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