Geodesic
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1185-1195

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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.

Classification : 65J99, 65Z05
Keywords: Min-plus eigenvalue problems, numerical analysis, Frenkel-kontorova model, Hamilton-Jacobi equations 
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     author = {Baca\"er, Nicolas},
     title = {Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, {Frenkel-Kontorova} models and homogenization of {Hamilton-Jacobi} equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1185--1195},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {6},
     year = {2001},
     mrnumber = {1873522},
     zbl = {1037.65054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1185_0/}
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Bacaër, Nicolas. Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1185-1195. http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1185_0/