Large-time behavior of solutions of Lax-Friedrichs finite difference equations for hyperbolic systems of conservation laws

Author:
I-Liang Chern

Journal:
Math. Comp. **56** (1991), 107-118

MSC:
Primary 65M12; Secondary 35L65, 39A12, 76L05

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052088-8

MathSciNet review:
1052088

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Abstract: We study the large-time behavior of discrete solutions of the Lax-Friedrichs finite difference equations for hyperbolic systems of conservation laws. The initial data considered here are small and tend to a constant state at . We show that the solutions tend to the *discrete diffusion waves* at the rate in , , with being an arbitrarily small constant. The discrete diffusion waves can be constructed from the self-similar solutions of the heat equation and the Burgers equation through an averaging process.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052088-8

Keywords:
Lax-Friedrichs scheme,
hyperbolic systems of conservation laws,
discrete diffusion waves,
asymptotic behavior,
numerical viscosity

Article copyright:
© Copyright 1991
American Mathematical Society