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

Published online by Cambridge University Press:  12 July 2007

Bogdan Craciun  and
Kaushik Bhattacharya
Bogdan Craciun
Affiliation:
Synopsys, 700 E. Middlefield Road, Mountain View, CA 94043-4033, USA ([email protected])
Kaushik Bhattacharya
Affiliation:
Division of Engineering and Applied Science, Mail Stop 104-44, California Institute of Technology, Pasadena, CA 91125, USA ([email protected])
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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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