Eulerian, Lagrangian and broad continuous solutions to a balance law with non convex flux II

We consider a continuous solution u of the balance law in one space dimension, where the flux function f is of class C^2 and the source term is bounded. This equation admits an Eulerian interpretation (namely the distributional one) and a Lagrangian interpretation (which can be further specified). Since u is only continuous, these interpretations do not necessarily agree; moreover each interpretation naturally entails a different equivalence class for the source term g. In this paper we com- plete the comparison between these notions of solutions started in the companion paper [G. Alberti, S. Bianchini and L. Caravenna, Eulerian, lagrangian and broad continuous solutions to a balance law with non convex flux I, J. Differ. Equ. 261 (2016) 4298–4337], and analize in detail the relations between the corresponding notions of source term