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An Explicit Lower Bound for Blow Up Time in a Class of Nonlinear Wave Equations with Nonlinear Damping and Source Terms

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Abstract

This paper deals with an initial boundary value problem for a class of nonlinear wave equation with nonlinear damping and source terms whose solution may blow up in finite time. An explicit lower bound for blow up time is determined by means of a differential inequality argument if blow up occurs.

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Acknowledgments

The authors are grateful to the anonymous referees for the constructive comments and useful suggestions.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Xiao-ming Peng

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Ya-dong Shang

  3. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Xue-qin Wang

Authors
  1. Xiao-ming Peng
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  2. Ya-dong Shang
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  3. Xue-qin Wang
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Corresponding author

Correspondence to Ya-dong Shang.

Additional information

This work is supported by big data and Educational Statistics Application Laboratory (2017WSYS001), Guangdong University of Finance and Economics.

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Peng, Xm., Shang, Yd. & Wang, Xq. An Explicit Lower Bound for Blow Up Time in a Class of Nonlinear Wave Equations with Nonlinear Damping and Source Terms. Acta Math. Appl. Sin. Engl. Ser. 37, 148–154 (2021). https://doi.org/10.1007/s10255-021-0995-y

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  • DOI: https://doi.org/10.1007/s10255-021-0995-y

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