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

  • Alaeddin Draifia
  • Abderrahmane Zarai
  • Salah Boulaaras
Article

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.

Keywords

Viscoelastic equations Global existence General decay 

Mathematics Subject Classification

35L35 35L20 

Notes

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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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  • Alaeddin Draifia
    • 1
  • Abderrahmane Zarai
    • 1
  • Salah Boulaaras
    • 2
    • 3
  1. 1.Laboratory of Mathematics, Informatics and Systems (LAMIS), Department of Mathematics and Computer ScienceLarbi Tebessi UniversityTebessaAlgeria
  2. 2.Department of Mathematics, College of Sciences and Arts, Al-RassQassim UniversityBuraidahKingdom of Saudi Arabia
  3. 3.Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO)University of Oran 1OranAlgeria

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