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Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface. (English) Zbl 1043.35028
This paper studies the overall evolution of fronts propagating with a normal velocity that depends on position, \(v_n= f(x)\), 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.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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