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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.

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