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Well-posedness and general decay for Moore–Gibson–Thompson equation in viscoelasticity with delay term

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Abstract

The problem of Moore–Gibson–Thompson equation with infinite memory and time delay terms is considered. Under suitable Lyapunov functionals with an appropriate assumptions on the kernel function and on the weight of the delay, we prove the well-posedness and the exponential stability of the system.

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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 to improve the paper.

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Authors and Affiliations

  1. Department of Sciences and Technology, University of Hassiba Ben Bouali, Chlef, Algeria

    Abdelkader Braik

  2. Department of Mathematics, BP 284, University Centre BELHADJ Bouchaib Ain Tmouchent, 46000, Ain Tmouchent, Algeria

    Abderrahmane Beniani

  3. Department of Mathematics, College of Sciences and Arts, Qassim University, Ar Rass, Saudi Arabia

    Khaled Zennir

  4. Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401, 24000, Guelma, Algérie

    Khaled Zennir

Authors
  1. Abdelkader Braik
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  2. Abderrahmane Beniani
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  3. Khaled Zennir
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Correspondence to Khaled Zennir.

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Braik, A., Beniani, A. & Zennir, K. Well-posedness and general decay for Moore–Gibson–Thompson equation in viscoelasticity with delay term. Ricerche mat 71, 689–710 (2022). https://doi.org/10.1007/s11587-021-00561-9

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  • DOI: https://doi.org/10.1007/s11587-021-00561-9

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