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Dispersive Estimates and Asymptotic Behavior for a Generalized Boussinesq-Type Equation

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Abstract

In this paper, we study the Cauchy problem for a generalized Boussinesq-type equation in \(\mathbb {R}^n\). We establish a dispersive estimate for the linear group associated with the generalized Boussinesq-type equation. As applications, the global existence, decay and scattering of solutions are established for small initial data.

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Acknowledgements

The first author is supported by the National Natural Science Foundation of China (Grant No. 12001073), the China Postdoctoral Science Foundation (Grant 2022M722105), the Natural Science Foundation of Chongqing (Grant Nos. cstc2020jcyj-msxmX0709 and cstc2020jcyj-jqX0022) and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant Nos. KJQN202200563 and KJZD-K202100503).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

    Guowei Liu & Wei Wang

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  1. Guowei Liu
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  2. Wei Wang
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Correspondence to Guowei Liu.

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Communicated by Rosihan M. Ali.

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Liu, G., Wang, W. Dispersive Estimates and Asymptotic Behavior for a Generalized Boussinesq-Type Equation. Bull. Malays. Math. Sci. Soc. 46, 174 (2023). https://doi.org/10.1007/s40840-023-01567-2

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  • DOI: https://doi.org/10.1007/s40840-023-01567-2

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