Selection problems of Z2 -periodic entropy solutions and viscosity solutions

研究成果: Article査読

4 被引用数 (Scopus)

抄録

Z2-periodic entropy solutions of hyperbolic scalar conservation laws and Z2-periodic viscosity solutions of Hamilton–Jacobi equations are not unique in general. However, uniqueness holds for viscous scalar conservation laws and viscous Hamilton–Jacobi equations. Bessi (Commun Math Phys 235:495–511, 2003) investigated the convergence of approximate Z2-periodic solutions to an exact one in the process of the vanishing viscosity method, and characterized this physically natural Z2-periodic solution with the aid of Aubry–Mather theory. In this paper, a similar problem is considered in the process of the finite difference approximation under hyperbolic scaling. We present a selection criterion different from the one in the vanishing viscosity method, which may depend on the approximation parameter.

本文言語English
論文番号119
ジャーナルCalculus of Variations and Partial Differential Equations
56
4
DOI
出版ステータスPublished - 2017 8 1

ASJC Scopus subject areas

  • 分析
  • 応用数学

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