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

Free access article

Issue		ESAIM: M2AN Volume 35, Number 6, November-December 2001


Page(s)		1185 - 1195
DOI		10.1051/m2an:2001153

DOI: 10.1051/m2an:2001153

M2AN, Vol. 35, N°6, pp. 1185-1195

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

Nicolas Bacaër

Université Paris 6, Laboratoire d'Analyse Numérique, 175 rue du chevaleret, 75013 Paris, France. (bacaer@ann.jussieu.fr)

(Received: June 25, 2001. Revised: August 16, 2001.)

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.

AMS Subject: 65J99, 65Z05.

Key words: Min-plus eigenvalue problems, numerical analysis, Frenkel-Kontorova model, Hamilton-Jacobi equations.

© EDP Sciences, SMAI 2001

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