Effective motion of a curvature-sensitive interface through a heterogeneous medium
Bogdan Craciun, Kaushik Bhattacharya · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2004
This paper deals with the evolution of fronts or interfaces propagating with normal velocity v n = fcκ, where f is a spatially periodic function, c a constant and κ the mean curvature.This study is motivated by the propagation of phase boundaries and dislocation loops through heterogeneous media.We establish a homogenization result when the scale of oscillation of f is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law v n = f (n).We illustrate the results using examples.We also provide an explicit characterization of f in the limit c → ∞.