Difference approximation to Aubry-Mather sets of the forced Burgers equation

Takaaki Nishida, Kohei Soga

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)2401-2422
Number of pages22
JournalNonlinearity
Volume25
Issue number9
DOIs
Publication statusPublished - 2012 Sep 1
Externally publishedYes

ASJC Scopus subject areas

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

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