# zbMATH — the first resource for mathematics

Pinning and de-pinning phenomena in front propagation in heterogeneous media. (English) Zbl 1101.35074
Summary: 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.

##### MSC:
 35Q72 Other PDE from mechanics (MSC2000) 74N20 Dynamics of phase boundaries in solids 35K57 Reaction-diffusion equations
Full Text: