Volume 6, Issue 1
Long-time Asymptotic Behavior of Lax-Friedrichs Scheme

Ying Lungan, Zhou Tie

J. Part. Diff. Eq.,6(1993),pp.39-61

Published online: 1993-06

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  • Abstract
In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I³ and I¹. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l² stability and l¹ boundedness.
  • Keywords

Lax-Friedrichs scheme discrete travelling waves asymptotic stability hyperbolic conservation laws energy method

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@Article{JPDE-6-39, author = {Ying Lungan, Zhou Tie}, title = {Long-time Asymptotic Behavior of Lax-Friedrichs Scheme}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {1}, pages = {39--61}, abstract = { In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I³ and I¹. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l² stability and l¹ boundedness.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5699.html} }
TY - JOUR T1 - Long-time Asymptotic Behavior of Lax-Friedrichs Scheme AU - Ying Lungan, Zhou Tie JO - Journal of Partial Differential Equations VL - 1 SP - 39 EP - 61 PY - 1993 DA - 1993/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5699.html KW - Lax-Friedrichs scheme KW - discrete travelling waves KW - asymptotic stability KW - hyperbolic conservation laws KW - energy method AB - In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I³ and I¹. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l² stability and l¹ boundedness.
Ying Lungan, Zhou Tie. (1970). Long-time Asymptotic Behavior of Lax-Friedrichs Scheme. Journal of Partial Differential Equations. 6 (1). 39-61. doi:
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