Abstract
The paper deals with the proof of the global existence of solutions for system of nonlinear viscoelastic Kirchhoff system with a distributed delay and general coupling terms in a bounded domain. The current study was performed by using the energy method along with Faedo–Galerkin method and under some suitable conditions in coupling terms parameters. In addition, we prove the stability result by using the multiplier 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. The second author would like to thank all the professors of the mathematics department at the University of Annaba in Algeria, especially his Professors/Scientists Pr. Mohamed Haiour, Pr. Ahmed-Salah Chibi, and Pr. Azzedine Benchettah for the important content of masters and PhD courses in pure and applied mathematics which he received during his studies. Moreover, he thanks them for the additional help they provided to him during office hours in their office about the few concepts/difficulties he had encountered, and he appreciates their talent and dedication for their postgraduate students currently and previously. In addition, the idea and research project in this paper was presented by the second author and was carried out by the both authors.
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On the occasion of the 80th birthday of the second author’s mother, Mrs. Fatma Bint Al-Tayeb Zeghdoud.
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Doudi, N., Boulaaras, S. Global existence combined with general decay of solutions for coupled Kirchhoff system with a distributed delay term. RACSAM 114, 204 (2020). https://doi.org/10.1007/s13398-020-00938-9
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DOI: https://doi.org/10.1007/s13398-020-00938-9
Keywords
- Global existence
- Lyapunov functional
- Faedo–Galerkin method
- General Decay
- Kirchhoff system
- Distributed delay term
- Viscoelastic term