Entropy conditions for quasilinear first order equations on nonlinear fiber bundles with special emphasis on the equation of 2D flat projective structure. II

Abstract

We find, in an intrinsic form, a generalized Rankine-Hugoniot condition with respect to an entropy density that allows to give the proper interpretation to a formula of Vol'pert reducing the entropy condition on a function with bounded variation to its expression for generic simple jumps. It also leads to define the conservation laws only in terms of characteristics and to point out the class of entropy conditions coming from oriented conservation laws.