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 T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}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. -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.

1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400484nas a2200133 4500008004100000245009400041210006900135260001900204300001200223490000800235100002300243700001200266856007200278 2014 en d00aStructure of entropy solutions to general scalar conservation laws in one space dimension0 aStructure of entropy solutions to general scalar conservation la bSISSAc08/2015 a356-3860 v4281 aBianchini, Stefano1 aYu, Lei uhttps://www.sciencedirect.com/science/article/pii/S0022247X1500221800932nas a2200109 4500008004100000245011500041210006900156260001000225520044500235100001200680856013000692 2013 en d00aThe structure and regularity of admissible BV solutions to hyperbolic conservation laws in one space dimension0 astructure and regularity of admissible BV solutions to hyperboli bSISSA3 aThis thesis is devoted to the study of the qualitative properties of admissible BV solutions to the strictly hyperbolic conservation laws in one space dimension by using wave-front tracking approximation. This thesis consists of two parts: • SBV-like regularity of vanishing viscosity BV solutions to strict hyperbolic systems of conservation laws. • Global structure of admissible BV solutions to strict hyperbolic conservation laws.1 aYu, Lei uhttps://www.math.sissa.it/publication/structure-and-regularity-admissible-bv-solutions-hyperbolic-conservation-laws-one-space00509nas a2200121 4500008004100000245009900041210006900140300001400209490000700223100002300230700001200253856012200265 2012 eng d00aSBV-like regularity for general hyperbolic systems of conservation laws in one space dimension0 aSBVlike regularity for general hyperbolic systems of conservatio a439–4720 v441 aBianchini, Stefano1 aYu, Lei uhttps://www.math.sissa.it/publication/sbv-regularity-general-hyperbolic-systems-conservation-laws-one-space-dimension