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$ L\sp 1$-stability of stationary discrete shocks


Authors: Jian-Guo Liu and Zhou Ping Xin
Journal: Math. Comp. 60 (1993), 233-244
MSC: Primary 35L65; Secondary 35L67, 65M12
DOI: https://doi.org/10.1090/S0025-5718-1993-1159170-7
MathSciNet review: 1159170
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Abstract: The nonlinear stability in the $ {L^p}$-norm, $ p \geq 1$, of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general $ m \times m$ systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1159170-7
Keywords: Lax-Friedrichs scheme, hyperbolic systems of conservation laws, discrete shock profiles, nonlinear stability
Article copyright: © Copyright 1993 American Mathematical Society

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