Abstract
We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i. e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.
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Foundation item: Supported by the National Natural Science Foundation of China (10131050), Science and Technology Committee of Shanghai, China (03JC14013)
Biography: LIU Yongqin (1979-), female, Ph. D. candidate, research direction: partial differential equation
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Yongqin, L., Weike, W. On the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Wuhan Univ. J. Nat. Sci. 11, 451–455 (2006). https://doi.org/10.1007/BF02836641
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DOI: https://doi.org/10.1007/BF02836641