We consider a continuous solution u of the balance law
∂tu+∂x(f(u))=g
in one space dimension, where the flux function f is of class C2 and the source term g is bounded. This equation admits an Eulerian intepretation (namely the distributional one) and a Lagrangian intepretation (which can be further specified). Since u is only continuous, these interpretations do not necessessarily agree; moreover each interpretation naturally entails a different equivalence class for the source term g. In this paper we complete the comparison between these notions of solutions started in the companion paper [Alberti-Bianchini-Caravenna I], and analize in detail the relations between the corresponding notions of source term.

Accepted on Journal of Hyperbolic Differential Equations