Selection problems of Z2 -periodic entropy solutions and viscosity solutions

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3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number119
JournalCalculus of Variations and Partial Differential Equations
Volume56
Issue number4
DOIs
Publication statusPublished - 2017 Aug 1

Fingerprint

Viscosity Method
Vanishing Viscosity
Scalar Conservation Laws
Entropy Solution
Hamilton-Jacobi Equation
Viscosity Solutions
Periodic Solution
Entropy
Viscous Conservation Laws
Viscosity
Hyperbolic Conservation Laws
Finite Difference Approximation
Conservation
Uniqueness
Scaling
Approximation

Keywords

  • 35L65
  • 37J50
  • 49L25
  • 60G50
  • 65M06

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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