UNIQUENESS OF GLOBALLY CONSERVATIVE WEAK SOLUTIONS FOR A WEAK DISSIPATION CAMASSA-HOLM TYPE EQUATION

Yonghui Zhou

doi:10.11948/20260196

2027 Volume 17 Issue 2

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Yonghui Zhou. UNIQUENESS OF GLOBALLY CONSERVATIVE WEAK SOLUTIONS FOR A WEAK DISSIPATION CAMASSA-HOLM TYPE EQUATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 998-1013. doi: 10.11948/20260196

Citation:

Yonghui Zhou. UNIQUENESS OF GLOBALLY CONSERVATIVE WEAK SOLUTIONS FOR A WEAK DISSIPATION CAMASSA-HOLM TYPE EQUATION[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 998-1013. doi: 10.11948/20260196

UNIQUENESS OF GLOBALLY CONSERVATIVE WEAK SOLUTIONS FOR A WEAK DISSIPATION CAMASSA-HOLM TYPE EQUATION

Yonghui Zhou^1, ,

1.
School of Mathematics, Hexi University, Zhangye 734000, China

Corresponding author: Email: zhouyhmath@163.com(Y. Zhou)
Fund Project: The authors were supported by National Natural Science Foundation of China (12501210), Natural Science Foundation of Gansu Province (26JRRG010), Doctoral Research Foundation of Hexi University (KYQD2025006), Zhangye Science and Technology Plan Project (ZY2025BJ05), the Fundamental Research Funds for Heilongjiang Proviencial Universities (No. 2025-KYYWF-ZR0134), and Innovation Fund for University Teachers of Gansu Province (2026B-193)

Abstract

Abstract

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 $H^{1}$ space.
- Dispersive wave equations /
- globally conservative solutions /
- uniqueness
MSC: 35A02, 35Q35

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References

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