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 I&sup3 and I&sup1. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l&sup2 stability and l&sup1 boundedness.