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.
|Calculus of Variations and Partial Differential Equations
|Published - 2017 Aug 1
ASJC Scopus subject areas
- Applied Mathematics