We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton–Jacobi equations can be approximated by iterated twisted Lax–Oleinik like operators. We establish convergence to the solution of the iterated scheme and discuss further properties of the approximate solutions.
Nous démontrons que les solutions de viscosité d’un système faiblement couplé d’équations d’Hamilton–Jacobi peuvent être approchées par des itérations d’opérateurs tordus à la Lax–Oleinik. On établit la convergence vers la solution du schéma itératif et mettons en exergue quelques propriétés supplémentaires des solutions approchées.
Accepted:
Published online:
DOI: 10.5802/afst.1598
Keywords: weakly coupled systems of Hamilton–Jacobi equations, viscosity solutions, weak KAM Theory
Maxime Zavidovique 1
CC-BY 4.0
@article{AFST_2019_6_28_2_209_0,
author = {Maxime Zavidovique},
title = {Twisted {Lax{\textendash}Oleinik} formulas and weakly coupled systems of {Hamilton{\textendash}Jacobi} equations},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {209--224},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 28},
number = {2},
year = {2019},
doi = {10.5802/afst.1598},
mrnumber = {3957680},
zbl = {07095681},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1598/}
}
TY - JOUR AU - Maxime Zavidovique TI - Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 209 EP - 224 VL - 28 IS - 2 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1598/ DO - 10.5802/afst.1598 LA - en ID - AFST_2019_6_28_2_209_0 ER -
%0 Journal Article %A Maxime Zavidovique %T Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 209-224 %V 28 %N 2 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1598/ %R 10.5802/afst.1598 %G en %F AFST_2019_6_28_2_209_0
Maxime Zavidovique. Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 2, pp. 209-224. doi : 10.5802/afst.1598. https://afst.centre-mersenne.org/articles/10.5802/afst.1598/
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