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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, Serie 6, Volume 28 (2019) no. 2, pp. 209-224.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1598
Classification: 35F21,  49L25,  37J50
Keywords: weakly coupled systems of Hamilton–Jacobi equations, viscosity solutions, weak KAM Theory
Maxime Zavidovique 1

1 IMJ (projet Analyse Algébrique), UPMC, 4, place Jussieu, Case 247, 75252 Paris Cédex 5, France
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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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