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This paper is to study the asymptotic stability of stationary dis- crete shocks for the Lax-Friedrichs scheme approximating nonconvex scalar conservation laws, provided that the summations of the initial perturbations equal to zero. The result is proved by using a weighted energy method based on the nonconvexity. Moreover, the l1 stability is also obtained. The key points of our proofs are to choose a suitable weight function.

Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws