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

Abstract

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.

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