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General decay for a viscoelastic problem with not necessarily decreasing kernel

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Abstract

In this paper, a problem which arises in viscoelasticity is considered. We obtain the decay rate of the energy, for certain class of relaxation functions not necessarily exponentially or polynomially decaying to zero. Our results are natural generalizations of the previous ones in Medjden and Tatar (Appl Math Comput 67:1221–1235, 2005).

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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 for any decision. The second author gratefully acknowledge Qassim University in Kingdom of Saudi Arabia and this presented work is in memory of his father (1910–1999) Mr. Mahmoud ben Mouha Boulaaras.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Larbi Tebessi University, 12002, Tebessa, Algeria

    Fatiha Mesloub

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

    Salah Boulaaras

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

    Salah Boulaaras

Authors
  1. Fatiha Mesloub
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  2. Salah Boulaaras
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Correspondence to Salah Boulaaras.

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Mesloub, F., Boulaaras, S. General decay for a viscoelastic problem with not necessarily decreasing kernel. J. Appl. Math. Comput. 58, 647–665 (2018). https://doi.org/10.1007/s12190-017-1161-9

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  • DOI: https://doi.org/10.1007/s12190-017-1161-9

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