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 [1], we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolicity assumption.

[1] S.Bianchini, Interaction estimates and Glimm functional for general hyperbolic systems, Discrete Contin. Dyn. Syst., 9 (2003), pp. 133–166.