Structural Stability and Regularity of Entropy Solutions to Hyperbolic Systems of Conservation Laws

Abstract

The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm. We then consider a sequence of exact or approximate solutions uν, converging to a solution u in L1. The convergence of the wave-fronts of uν to the corresponding fronts of u is studied, proving a structural stability result in a neighborhood of each point in the t-x plane.