A note on the new Glimm functional for general systems of hyperbolic conservation laws
Jiale Hua and Tong Yang
Abstract: For systems of hyperbolic conservation laws, a new Glimm functional was recently constructed when the linearly degenerate manifold in each characteristic field is either the whole space or it consists of a finitely many smooth and transversal manifolds of co-dimension one. This new functional leads to the neat consistency and convergence rate estimation of the Glimm scheme. In this paper, by the motivation of the result in , we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolicity assumption.
 S.Bianchini, Interaction estimates and Glimm functional for general hyperbolic systems, Discrete Contin. Dyn. Syst., 9 (2003), pp. 133–166.