# 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 (2010)

- Volume: 35, Issue: 6, page 1185-1195
- ISSN: 0764-583X

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topBacaër, 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 35.6 (2010): 1185-1195. <http://eudml.org/doc/197454>.

@article{Bacaër2010,

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.
},

author = {Bacaër, Nicolas},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Min-plus eigenvalue problems; numerical analysis;
Frenkel-Kontorova model; Hamilton-Jacobi equations.; Frenkel-Kontorova models; min-plus integral eigenvalue problem; convergence; solid-state physics; homogenization; Hamilton-Jacobi equations},

language = {eng},

month = {3},

number = {6},

pages = {1185-1195},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/197454},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Bacaër, Nicolas

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 6

SP - 1185

EP - 1195

AB -
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.

LA - eng

KW - Min-plus eigenvalue problems; numerical analysis;
Frenkel-Kontorova model; Hamilton-Jacobi equations.; Frenkel-Kontorova models; min-plus integral eigenvalue problem; convergence; solid-state physics; homogenization; Hamilton-Jacobi equations

UR - http://eudml.org/doc/197454

ER -

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