Dirr, Nicolas P. ![]() |
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 |
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Date Type: | Publication |
Status: | Published |
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 |
Citation Data
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