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Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay

Author

Listed:
  • Danhua Wang

    (College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Gang Li

    (College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Biqing Zhu

    (College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

Abstract

In our previous work (Journal of Nonlinear Science and Applications 9: 1202–1215, 2016), we studied the well-posedness and general decay rate for a transmission problem in a bounded domain with a viscoelastic term and a delay term. In this paper, we continue to study the similar problem but without the frictional damping term. The main difficulty arises since we have no frictional damping term to control the delay term in the estimate of the energy decay. By introducing suitable energy and Lyapunov functionals, we establish an exponential decay result for the energy.

Suggested Citation

  • Danhua Wang & Gang Li & Biqing Zhu, 2016. "Exponential Energy Decay of Solutions for a Transmission Problem With Viscoelastic Term and Delay," Mathematics, MDPI, vol. 4(2), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:2:p:42-:d:71767
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    References listed on IDEAS

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    1. Wenjun Liu & Kewang Chen, 2016. "Existence and general decay for nondissipative hyperbolic differential inclusions with acoustic/memory boundary conditions," Mathematische Nachrichten, Wiley Blackwell, vol. 289(2-3), pages 300-320, February.
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