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A qualitative study and numerical simulations for a time-delayed dispersive equation

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Abstract

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the system exponentially converges to zero when the time tends to infinity provided that the time-delay is small and the damping term satisfies reasonable conditions. Lastly, an intensive numerical study is put forward and numerical illustrations of the stability result are provided.

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Acknowledgements

This work was supported and funded by Kuwait University, Research Grant No. SM05/18. The valuable corrections, suggestions, and comments from the editor and the anonymous referees are greatly appreciated.

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Authors and Affiliations

  1. UR Analysis and Control of PDEs, UR 13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia

    Kaïs Ammari

  2. Department of Mathematics, Faculty of Science, Kuwait University, 13060, Safat, Kuwait

    Boumediène Chentouf & Nejib Smaoui

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  1. Kaïs Ammari
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  2. Boumediène Chentouf
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Correspondence to Boumediène Chentouf.

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Ammari, K., Chentouf, B. & Smaoui, N. A qualitative study and numerical simulations for a time-delayed dispersive equation. J. Appl. Math. Comput. 66, 465–491 (2021). https://doi.org/10.1007/s12190-020-01446-0

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