Effective motion of a curvature-sensitive interface through a heterogeneous medium. (English) Zbl 1061.35148

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.


35Q72 Other PDE from mechanics (MSC2000)
74N20 Dynamics of phase boundaries in solids
35R35 Free boundary problems for PDEs
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