In this paper, we prove the uniqueness of globally conservative solutions for Camassa-Holm type equation by the analysis of characteristics. Giving a conservative solution, we introduce a set of auxiliary variables tailored to this solution, and prove that these variables satisfy a suitable semilinear system of equations. By proving that this semilinear system has a unique solution, we eventually obtain the uniqueness of the conservative solution of the original equation in time weighted H¹ space.
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Yonghui Zhou (2026) studied this question.
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