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

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Yip, N. K. 2006. Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces and Free Boundaries 8 (1) , pp. 79-109. 10.4171/IFB/136

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	European Mathematical Society Publishing House
ISSN:	1463-9963
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13077

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