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In this paper, we introduce a new Glimm functional for general systems of hyperbolic conservation laws. This new functional is consistent with the classical Glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate so that it can be viewed as " optimal " in some sense. With this new functional, the(More)
and Applied Analysis 3 Theorem 1.1. Given u0 x ∈ H R , s > 3/2, then there exist a T and a unique solution u to 1.1 such that u t, x ∈ C 0, T ;H R ∩ C1 ( 0, T ;Hs−1 R ) . 1.7 To make the paper concise we would like to omit the detailed proof, since one can find similar ones for these types of equations in 7, 24 . Whenwe study the Camassa-Holm equation,(More)
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