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Blow-up of the solutions of the initial boundary value problem of Camassa-Holm equation

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Wuhan University Journal of Natural Sciences

Abstract

Any classical non-null solution to the initial boundary value problem of Camassa-Holm equation on finite interval with homogeneous boundary condition must blow up in finite time. An initial boundary value problem of Camassa-Holm equation on half axis is also investigated in this paper. When the initial potential is nonnegative, then the classical solution exists globally; if the derivative of initial data on zero point is nonpositire, then the life span of nonzero solution must be finite.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, 430072, Wuhan, Hubei, China

    Zhu Xu-sheng & Wang Wei-ke

  2. Department of Mathematics, East China Jiaotong University, 330013, Nanchang, Jiangxi, China

    Zhu Xu-sheng

Authors
  1. Zhu Xu-sheng
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  2. Wang Wei-ke
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Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10131050)

Biography: ZHU Xu-sheng (1968-), male, Ph. D. candidate, research direction; partial differential equations.

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Xu-sheng, Z., Wei-ke, W. Blow-up of the solutions of the initial boundary value problem of Camassa-Holm equation. Wuhan Univ. J. Nat. Sci. 10, 961–965 (2005). https://doi.org/10.1007/BF02832448

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  • DOI: https://doi.org/10.1007/BF02832448

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