# Twisted Lax--Oleinik formulas and weakly coupled systems of Hamilton--Jacobi equations

## TL;DR

This paper introduces a method to approximate viscosity solutions of weakly coupled Hamilton--Jacobi systems using iterated twisted Lax--Oleinik operators, proving convergence and analyzing properties of the approximations.

## Contribution

It presents a novel iterative scheme for approximating solutions of coupled Hamilton--Jacobi systems and proves its convergence.

## Key findings

- Convergence of the iterated scheme to the true solution.
- Properties of the approximate solutions are characterized.
- The method extends classical Lax--Oleinik formulas to coupled systems.

## Abstract

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.