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Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation

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Abstract

In this paper, a class of nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo–Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given.

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Acknowledgements

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions which helped them to improve the paper.

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Authors and Affiliations

  1. Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, P.O.Box 89, 22000, Sidi Bel Abbés, Algeria

    Nadia Mezouar

  2. Faculty of Sciences Economics, Mustapha Stambouli University, 29000, Mascara, Algeria

    Nadia Mezouar

  3. Department of Mathematics, College of Sciences and Arts, Qassim University, Al-Rass, Kingdom of Saudi Arabia

    Salah Boulaaras

  4. Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Oran, Algeria

    Salah Boulaaras

Authors
  1. Nadia Mezouar
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  2. Salah Boulaaras
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Corresponding author

Correspondence to Salah Boulaaras.

Additional information

Communicated by Syakila Ahmad.

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Mezouar, N., Boulaaras, S. Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation. Bull. Malays. Math. Sci. Soc. 43, 725–755 (2020). https://doi.org/10.1007/s40840-018-00708-2

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  • DOI: https://doi.org/10.1007/s40840-018-00708-2

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