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

Takaaki Nishida, Kohei Soga

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2401-2422
ページ数22
ジャーナルNonlinearity
25
9
DOI
出版ステータスPublished - 2012 9
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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