Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-26T11:21:24.610Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)