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 -
References
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