Structure of the fundamental solution of a nonconvex conservation law

TL;DR

This paper investigates the detailed structure of fundamental solutions for nonconvex conservation laws, classifying shock and rarefaction wave interactions to understand the global dynamics without assuming convexity.

Contribution

It provides a comprehensive classification of wave interactions and a global dynamics framework for nonconvex fluxes in conservation laws, extending prior convexity-based analyses.

Findings

Classification of shocks and rarefaction waves

Analysis of wave interactions in nonconvex fluxes

Description of global dynamics using characteristic maps

Abstract

The structure of a signed fundamental solution of a conservation law is studied without the convexity assumption. The types of shocks and rarefaction waves are classified together with their interactions. A comprehensive picture of a global dynamics of a nonconvex flux is discussed in terms of characteristic maps and dynamical convex-concave envelopes.