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Published August 2003 | Published
Journal Article Open

Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface


This paper studies the overall evolution of fronts propagating with a normal velocity that depends on position, υ_n = f(x), where f is rapidly oscillating and periodic. A level-set formulation is used to rewrite this problem as the periodic homogenization of a Hamilton–Jacobi equation. The paper presents a series of variational characterization (formulae) of the effective Hamiltonian or effective normal velocity. It also examines the situation when f changes sign.

Additional Information

© 2003 The Royal Society of Edinburgh. MS received 17 January 2002; accepted 16 January 2003. Issued 22 August 2003. This work was conducted while B.C. was at the California Institute of Technology. It is our pleasure to thank Robert V. Kohn a very useful discussion. We gratefully acknowledge the support of the US 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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