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Decay of an Extensible Viscoelastic Plate Equation with a Nonlinear Time Delay

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Abstract

An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback, and source term, we establish a general decay of energy by using the multiplier method if the weight of weak dissipation and the delay satisfy \(\mu _2<\frac{\mu _1\alpha _1(1-d)}{\alpha _2(1-\alpha _1d)}\), and extend some known results.

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Acknowledgements

The authors express sincere thanks to the referees for their constructive comments and suggestions that helped to improve this paper. This work was supported by the National Natural Science Foundation of China (No. 11701465).

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Authors and Affiliations

  1. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Baowei Feng

  2. Department of Mathematics, College of Sciences and Arts, Al-Ras, Qassim University, Al-Mulida, Kingdom of Saudi Arabia

    Khaled Zennir

  3. Laboratory LAMAHIS, Department of Mathematics, University 20 Août 1955, 21000, Skikda, Algeria

    Khaled Zennir

  4. Department of Mathematics, University of Constantine 1, Constantine, Algeria

    Lakhdar Kassah Laouar

Authors
  1. Baowei Feng
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  2. Khaled Zennir
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  3. Lakhdar Kassah Laouar
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Correspondence to Baowei Feng.

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Communicated by Syakila Ahmad.

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Feng, B., Zennir, K. & Laouar, L.K. Decay of an Extensible Viscoelastic Plate Equation with a Nonlinear Time Delay. Bull. Malays. Math. Sci. Soc. 42, 2265–2285 (2019). https://doi.org/10.1007/s40840-018-0602-4

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  • DOI: https://doi.org/10.1007/s40840-018-0602-4

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