an:02103788
Zbl 1061.35148
Craciun, Bogdan; Bhattacharya, Kaushik
Effective motion of a curvature-sensitive interface through a heterogeneous medium
EN
Interfaces Free Bound. 6, No. 2, 151-173 (2004).
00104850
2004
j
35Q72 74N20 35R35
level-set formulation; effective motion; homogenization; curvature; trapped interfaces
The authors study propagating fronts or interfaces with normal velocity \(v_{n}=f(x)-c\kappa\), i.e. the normal velocity depends on a (periodic) function \(f\) and the mean curvature \(\kappa\). The problem is motivated, for instance, by the motion of a phase boundary through a heterogeneous material. For the homogenization of the problem they show that the interface propagates with normal velocity \(v_{n}=\bar{f}(n)\), in particular the normal velocity just depends on the normal \(n\) to the interface. Moreover, other features and examples like trapped interfaces are discussed, the limit of large curvature coefficients \(c\) is characterized in the last section.
Michael Bildhauer (Saarbr??cken)