The $l^1$ global decay to discrete shocks for scalar monotone schemes

Abstract

Abstract. Given a family of discrete shocks φ of a monotone scheme, we prove that the discrete shock profile with rational shock speed η is asymptotically stable with respect to the l 1 topology · 1 : if u 0 − φ ∈ l 1 , then u n − φ ·−nη 1 → 0 as n → ∞ under no restriction conditions of the initial data to the interval [inf φ, sup φ]. The asymptotic wave profile is uniquely identified from the above family by a mass parameter.