This paper deals with the evolution of fronts or interfaces propagating with normal velocity where is a spatially periodic function, a constant and 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 is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law . We illustrate the results using examples. We also provide an explicit characterization of in the limit .
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Bogdan Craciun, Kaushik Bhattacharya, Effective motion of a curvature-sensitive interface through a heterogeneous medium. Interfaces Free Bound. 6 (2004), no. 2, pp. 151–173