一类非线性时滞色散方程稳定性的定性和数值研究
Qualitative and numerical study of the stability of a nonlinear time-delayed dispersive equation
摘要：
研究了一类四阶非线性时滞色散方程的稳定性。首先，我们证明了系统的适定性，并给出了一些正则性结果。然后，我们证明了系统的零解指数收敛到零时，时间趋于无穷大的时间延迟是小的，阻尼项满足合理的条件。最后，提出了一个深入的数值研究，并提供了稳定性结果的数值例子。
英文摘要：
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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