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Global existence and decay of solutions of a singular nonlocal viscoelastic system

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Abstract

In this work, we consider a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition. By using the potential well theory we obtain the existence of a global solution. Then, we prove the general decay result, by constructing Lyapunov functional and using the perturbed energy method.

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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 Mathematics, Informatics and Systems (LAMIS), Department of Mathematics and Computer Science, Larbi Tebessi University, 12002, Tebessa, Algeria

    Alaeddin Draifia & Abderrahmane Zarai

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

    Salah Boulaaras

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

    Salah Boulaaras

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  1. Alaeddin Draifia
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  2. Abderrahmane Zarai
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  3. Salah Boulaaras
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Correspondence to Salah Boulaaras.

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Draifia, A., Zarai, A. & Boulaaras, S. Global existence and decay of solutions of a singular nonlocal viscoelastic system. Rend. Circ. Mat. Palermo, II. Ser 69, 125–149 (2020). https://doi.org/10.1007/s12215-018-00391-z

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  • DOI: https://doi.org/10.1007/s12215-018-00391-z

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