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Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations

Published online by Cambridge University Press:  15 April 2002

Nicolas Bacaër
Nicolas Bacaër*
Affiliation:
Université Paris 6, Laboratoire d'Analyse Numérique, 175 rue du chevaleret, 75013 Paris, France. (bacaer@ann.jussieu.fr)
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Abstract

Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized.

Keywords

Min-plus eigenvalue problemsnumerical analysisFrenkel-Kontorova modelHamilton-Jacobi equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 6 , November 2001 , pp. 1185 - 1195
Copyright
© EDP Sciences, SMAI, 2001

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