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Global existence and blow up for damped generalized Boussinesq equation

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Abstract

We study the Cauchy problem of damped generalized Boussinesq equation u tt − u xx + (u xx + f(u)) xx − αu xxt = 0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.

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Acknowledgements

We do appreciate the referee’s so many valuable suggestions, which corrected some mistakes in the paper and improved the paper a lot.

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Authors and Affiliations

  1. College of Science, Harbin Engineering University, Harbin, 150001, China

    Run-zhang Xu & Ji-hong Shen

  2. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Yong-bing Luo

  3. College of Computer Science and Technology, Harbin Engineering University, Harbin, 150001, China

    Shao-bin Huang

Authors
  1. Run-zhang Xu
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  2. Yong-bing Luo
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  3. Ji-hong Shen
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  4. Shao-bin Huang
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Corresponding author

Correspondence to Run-zhang Xu.

Additional information

Supported by the National Natural Science Foundation of China (11471087,11101102), Ph.D. Programs Foundation of Ministry of Education of China (20102304120022), the Support Plan for the Young College Academic Backbone of Heilongjiang Province (1252G020), the Natural Science Foundation of Heilongjiang Province (A201014), Science and Technology Research Project of Department of Education of Heilongjiang Province (12521401), Foundational Science Foundation of Harbin Engineering University and Fundamental Research Funds for the Central Universities.

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Xu, Rz., Luo, Yb., Shen, Jh. et al. Global existence and blow up for damped generalized Boussinesq equation. Acta Math. Appl. Sin. Engl. Ser. 33, 251–262 (2017). https://doi.org/10.1007/s10255-017-0655-4

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  • DOI: https://doi.org/10.1007/s10255-017-0655-4

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