Abstract
The nonlinear stability of stationary discrete shocks for the Lax-Friedrichs scheme approximating non-convex scalar conservation laws is proved without smallness restrictions on the initial perturbations provided that the summation of initial perturbation is zero. The long time behavior of the Lax-Friedrichs is also investigated for a rather broad class of initial data. The selection of the discrete weight function plays a crucial role. The detailed study of discrete error equations is a major technical involvement.
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