Linear orbital stability of discrete shock profiles for systems of conservation laws

Lucas Coeuret

Published 2023-11-04Version 1

We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on a precise description of the pointwise asymptotic behavior of the Green's function associated with those discrete shock profiles, improving on the result of Godillon [God03]. The main novelty of this stability result is that it applies for a fairly large family of schemes that introduce some artificial viscosity and most importantly, that we do not impose any weakness assumption on the shock.