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A qualitative study and numerical simulations for a time-delayed dispersive equation
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2020-10-21 , DOI: 10.1007/s12190-020-01446-0
Kaïs Ammari , Boumediène Chentouf , Nejib Smaoui

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.



中文翻译:

时滞色散方程的定性研究和数值模拟

本文研究了四阶非线性时滞色散方程的稳定性。首先,我们证明系统的适定性并给出一些规律性结果。然后,我们证明,当时间趋于无穷大时,只要时延较小且阻尼项满足合理条件,则系统的零解将收敛到零。最后,进行了深入的数值研究,并对稳定性结果进行了数值说明。

更新日期:2020-10-30
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