### Abstract

Jauslin-Kreiss-Moser andWE made clear the connection between the Aubry-Mather theory and the inviscid forced Burgers equation with a ℤ ^{2}-periodic forcing term and established the smooth approximation of ℤ ^{2}-periodic entropy solutions of the PDE. This paper presents results of a difference approximation to the Aubry-Mather sets. We prove the convergence of the Lax-Friedrichs scheme for the ℤ ^{2}-periodic entropy solutions. This result leads to difference approximations of the corresponding effective Hamiltonian and ℤ ^{2}-periodic viscosity solutions of the Hamilton-Jacobi equation. We numerically construct the Aubry-Mather sets through the approximate entropy solutions, based on the dynamical properties of the Aubry-Mather sets.

Original language | English |
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Pages (from-to) | 2401-2422 |

Number of pages | 22 |

Journal | Nonlinearity |

Volume | 25 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2012 Sep 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

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## Cite this

*Nonlinearity*,

*25*(9), 2401-2422. https://doi.org/10.1088/0951-7715/25/9/2401