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Published June 2004 | public
Journal Article

Effective motion of a curvature-sensitive interface through a heterogeneous medium


This paper deals with the evolution of fronts or interfaces propagating with normal velocity v_n=f−cκ 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 → ∞.

Additional Information

© 2004 European Mathematical Society. Received 19 August 2001 and in revised form 28 January 2004. This work was carried out while BC was at the California Institute of Technology, and partially when both BC and KB were visiting the Isaac Newton Institute, Cambridge, UK. It is a pleasure to thank Prof. L. C. Evans for useful discussions. We are also grateful for the support of the U.S. National Science Foundation (CMS 9457573) and the Air-Force Office of Scientific Research through a MURI grant (F49602-98-1-0433).

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