Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws

摘要

AbstractA system of quasi‐linear first‐order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly concave entropy function is analysed. In the class BV, i.e. a subset of regular distributions represented by functions of bounded variation in the sense of Tonelli‐Cesari, a weak solution to the system is defined. The parabolized version of the system is also discussed in order to define an admissible weak solution as a limit of a sequence of Lipschitz continuous solutions to the parabolic problem. It is proved that an admissible weak solution of the Cauchy problem is unique in the cla