Existence of semi-discrete shocks
A semi-discretization in space of a system of conservation laws is considered to construct discrete shocks. An existence theorem is proved for discrete shock profiles of small strength. An associated infinite-dimensional dynamical system is studied through the center manifold theorem. The semi-discrete shocks are proved to be heteroclinic orbits on the center manifold exhibited. The results are valid for the Godunov and Lax-Friedrichs schemes.
heteroclinic orbits on the center manifold
scientific article; zbMATH DE number 1736525