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Twisted Lax–Oleinik formulas and weakly coupled systems of Hamilton–Jacobi equations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 2, pp. 209-224.

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.

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.

Reçu le : 2017-04-04
Accepté le : 2017-04-23
Publié le : 2019-05-02
DOI : https://doi.org/10.5802/afst.1598
Classification : 35F21,  49L25,  37J50
Mots clés: weakly coupled systems of Hamilton–Jacobi equations, viscosity solutions, weak KAM Theory
@article{AFST_2019_6_28_2_209_0,
     author = {Maxime Zavidovique},
     title = {Twisted Lax--Oleinik formulas and weakly coupled systems of Hamilton--Jacobi equations},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {2},
     year = {2019},
     pages = {209-224},
     doi = {10.5802/afst.1598},
     zbl = {07095681},
     mrnumber = {3957680},
     language = {en},
     url = {afst.centre-mersenne.org/item/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, Série 6, Tome 28 (2019) no. 2, pp. 209-224. doi : 10.5802/afst.1598. https://afst.centre-mersenne.org/item/AFST_2019_6_28_2_209_0/

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