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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

Nicolas Bacaër — 2001

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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....

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

Nicolas Bacaër — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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...

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