This paper addresses the impact of the presence of a boundary memory term in the third-order Korteweg–de Vries equation in a bounded interval \([0,\ell ]\). First, an overall literature review is provided. Indeed, a comprehensive discussion on the literature constitutes a survey part of the current paper. Thereafter, it is shown that the system under consideration possesses a unique solution under a smallness assumption on the initial data and an appropriate condition on the parameters and the kernel involved in the memory term. Last but not least, we demonstrate that the zero solution is exponentially stable as long as the length \(\ell \) is small enough by means of Lyapunov method, which permits to provide an estimate of the exponential decay rate. These findings improve and complement those of Zhang (in: Desch W, Kappel F, Kunisch K (eds) Proceedings of international conference on control and estimation of distributed parameter systems: nonlinear phenomena, International Series of Numerical Mathematics, vol 118, Birkhauser, Basel, pp 371–389, 1994) (resp. Baudouin et al. in IEEE Trans Autom Control 64:1403–1414, 2019), where no memory term is present (resp. a delay occurs instead of memory).

本文讨论了在有界区间\（[0，\ ell] \）中三阶Korteweg-de Vries方程中边界记忆项的存在的影响。首先，提供全面的文献综述。确实，对文献的全面讨论构成了本文的调查部分。此后，表明所考虑的系统在初始数据较小的假设下以及在存储项中涉及的参数和内核的适当条件下具有唯一的解决方案。最后但并非最不重要的一点是，我们证明了只要长度\（\ ell \）零解都是指数稳定的利用李雅普诺夫方法可以将其减小到足够小，该方法可以提供指数衰减率的估计值。这些发现改进和补充了张的发现（在：Desch W，Kappel F，Kunisch K（eds）上，国际会议对分布参数系统的控制和估计：非线性现象，国际数值数学系列，第118卷，Birkhauser，巴塞尔，第371–389页，1994年）（Baudouin等人，在IEEE Trans Autom Control 64：1403–1414，2019中），其中不存在记忆项（代表发生延迟而不是记忆）。