Homogenization of a Hamilton–Jacobi equation associated with the geometric motion of an interface
Published online by Cambridge University Press: 12 July 2007
Abstract
This paper studies the overall evolution of fronts propagating with a normal velocity that depends on position, υn = 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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 4 , August 2003 , pp. 773 - 805
- Copyright
- Copyright © Royal Society of Edinburgh 2003
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