2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143298This note is devoted to the explicit construction of a functional defined on all pairs of $\L1$ functions with small total variation, which is equivalent to the $\L1$ distance and non increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional by Bressan, Liu and Yang.26 pagesAnalysis of PDEs35L65text