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

TL;DR

This paper develops an intrinsic generalized Rankine-Hugoniot condition for entropy in quasilinear first order equations on nonlinear fiber bundles, connecting entropy conditions with characteristics and conservation laws.

Contribution

It introduces a new intrinsic entropy condition framework and relates it to conservation laws and characteristics for complex geometric PDEs.

Findings

Generalized Rankine-Hugoniot condition formulated

Entropy conditions linked to characteristics and conservation laws

Reduction of entropy condition to simple jumps in BV functions

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.