Selection problems of Z^2-periodic entropy solutions and viscosity solutions

Kohei Soga

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arXiv · 1501.03594

Selection problems of Z^2-periodic entropy solutions and viscosity solutions

Kohei Soga

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Abstract

Z^2-periodic entropy solutions of hyperbolic scalar conservation laws and Z^2-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. Ugo Bessi ('03) investigated the convergence of approximate Z^2-periodic solutions to an exact one in the process of the vanishing viscosity method, and characterized this physically natural Z^2-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 exhibits difference in characteristics between the two approximation techniques.

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Kohei Soga. 2015-01-15. Selection problems of Z^2-periodic entropy solutions and viscosity solutions. https://arxiv.org/abs/1501.03594

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