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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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
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 $ x = \pm \infty $. We show that the solutions tend to the discrete diffusion waves at the rate $ O({t^{ - 3/4 + 1/2p + \sigma }})$ in $ {l^p}$, $ 1 \leq p \leq \infty $, with $ \sigma > 0$ 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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1052088-8
PII: S 0025-5718(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