Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws

Liu, Hailiang; Wang, Jinghua

doi:10.1090/S0025-5718-96-00733-8

Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws
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by Hailiang Liu and Jinghua Wang PDF

Math. Comp. 65 (1996), 1137-1153 Request permission

Abstract:

This paper is to study the asymptotic stability of stationary discrete 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 $l^1$ stability is also obtained. The key points of our proofs are to choose a suitable weight function.

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