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 semilinear and reaction-diffusion equations.
Original language | English |
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Pages (from-to) | 79-109 |
Number of pages | 31 |
Journal | Interfaces and Free Boundaries |
Volume | 8 |
Issue number | 1 |
Publication status | Published - 2006 |