On the structure of solutions for general hyperbolic systems of balance laws

TL;DR

This paper analyzes the wave-front structure of BV entropy solutions for hyperbolic balance laws, extending previous results to systems with both genuinely nonlinear and linearly degenerate fields, using fractional step schemes and wave-front tracking.

Contribution

It provides a detailed description of the local and global wave-front structure for solutions of hyperbolic balance laws, extending prior work on conservation laws.

Findings

Characterization of wave-front structure in BV solutions

Extension of wave-front tracking methods to balance laws

Detailed analysis of solutions with mixed characteristic fields

Abstract

The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results by Binahcini and Yu for strictly hyperbolic systems of conservation laws.