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Asymptotic Profile of Solutions to the Degasperis–Procesi Equation

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Abstract

It is shown that a strong solution of the Degasperis–Procesi equation, initially decaying exponentially together with its spatial derivative, must be identically equal to zero if it also decays exponentially at a later time. The decay rate of the corresponding strong solution at infinity is also given for some kinds of initial data with exponential decay.

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Acknowledgments

The authors thank the referees for their careful reading and suggestions on this manuscript. This work was partially supported by Natural Science Foundation of China under Grant Nos. 11301394 and 11226172, Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ12A01009 and the National Basic Research Program of China under Grant No. 2012CB426510.

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Authors and Affiliations

  1. Xinglin College, NanTong University, Nantong, 226007, Jiangsu, China

    Huiping Chen

  2. College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, Zhejiang, China

    Zhengguang Guo

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  1. Huiping Chen
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  2. Zhengguang Guo
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Correspondence to Zhengguang Guo.

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Communicated by Yong Zhou.

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Chen, H., Guo, Z. Asymptotic Profile of Solutions to the Degasperis–Procesi Equation . Bull. Malays. Math. Sci. Soc. 38, 333–344 (2015). https://doi.org/10.1007/s40840-014-0023-y

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  • DOI: https://doi.org/10.1007/s40840-014-0023-y

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