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

  • Baowei Feng
  • Khaled Zennir
  • Lakhdar Kassah Laouar
Article

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.

Keywords

Plate equation Viscoelastic term Energy decay Nonlinear time-varying delay 

Mathematics Subject Classification

35B35 74Dxx 93D15 93D20 

Notes

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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  • Baowei Feng
    • 1
  • Khaled Zennir
    • 2
    • 3
  • Lakhdar Kassah Laouar
    • 4
  1. 1.Department of Economic MathematicsSouthwestern University of Finance and EconomicsChengduPeople’s Republic of China
  2. 2.Department of Mathematics, College of Sciences and ArtsAl-Ras, Qassim UniversityAl-MulidaKingdom of Saudi Arabia
  3. 3.Laboratory LAMAHIS, Department of Mathematics, University 20 Août 1955SkikdaAlgeria
  4. 4.Department of MathematicsUniversity of Constantine 1ConstantineAlgeria

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