Volume 35, Number 6, November/December 2001
|Page(s)||1185 - 1195|
|Published online||15 April 2002|
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Université Paris 6, Laboratoire d'Analyse
Numérique, 175 rue du chevaleret, 75013 Paris, France. (firstname.lastname@example.org)
Revised: 16 August 2001
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.
Mathematics Subject Classification: 65J99 / 65Z05
Key words: Min-plus eigenvalue problems / numerical analysis / Frenkel-Kontorova model / Hamilton-Jacobi equations.
© EDP Sciences, SMAI, 2001
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