Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension

摘要

The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves ? such that outside ?∪ Θ the solution is continuous, and for all points in ?Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. L_(loc)~1-convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.