$L^ 1$-stability of stationary discrete shocks
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- by Jian-Guo Liu and Zhou Ping Xin PDF
- Math. Comp. 60 (1993), 233-244 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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