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Asymptotic profile of global solutions to the generalized double dispersion equation via the nonlinear term

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Abstract

In this paper, we investigate the initial value problem for the generalized double dispersion equation in \({\mathbb {R}}^n\). Weighted decay estimate and asymptotic profile of global solutions are established for \(n\ge 3 \). The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233–254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.

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Acknowledgements

Y. Wang was supported in part by the NNSF of China (Grant No. 11101144), Innovation Scientists and Technicians Troop Construction Projects of Henan Province (Grant No. 14HASTIT041) and Plan For Scientific Innovation Talent of Henan Province (Grant No. 154100510012). C. Wei was supported in part by NSFC (Grant No. 11701517) and the Scientific Research Foundation of Zhejiang Sci-Tech University (Grant No. 16062021-Y).

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Authors and Affiliations

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China

    Yu-Zhu Wang

  2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Changhua Wei

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  1. Yu-Zhu Wang
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  2. Changhua Wei
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Correspondence to Changhua Wei.

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Wang, YZ., Wei, C. Asymptotic profile of global solutions to the generalized double dispersion equation via the nonlinear term. Z. Angew. Math. Phys. 69, 34 (2018). https://doi.org/10.1007/s00033-018-0930-0

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  • DOI: https://doi.org/10.1007/s00033-018-0930-0

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