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

Craciun, Bogdan and Bhattacharya, Kaushik (2003) Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 133 (4). pp. 773-805. ISSN 0308-2105. https://resolver.caltech.edu/CaltechAUTHORS:20131007-100104548

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1017/S0308210500002675 DOIArticle
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1202392PublisherArticle
ORCID:
AuthorORCID
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 2003 The Royal Society of Edinburgh. MS received 17 January 2002; accepted 16 January 2003. Issued 22 August 2003. This work was conducted while B.C. was at the California Institute of Technology. It is our pleasure to thank Robert V. Kohn a very useful discussion. We gratefully acknowledge the support of the US National Science Foundation (CMS 9457573) and the Air-Force Office of Scienti­fic Research through a MURI grant (F49602-98-1-0433).
Funders:
Funding AgencyGrant Number
NSFCMS 9457573
Air Force Office of Scientific Research (AFOSR)F49602-98-1-0433
Issue or Number:4
Record Number:CaltechAUTHORS:20131007-100104548
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131007-100104548
Official Citation:Bogdan Craciun and Kaushik Bhattacharya (2003). Homogenization of a Hamilton–Jacobi equation associated with the geometric motion of an interface. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 133, pp 773-805. doi:10.1017/S0308210500002675.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41704
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Oct 2013 17:24
Last Modified:03 Oct 2019 05:51

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