In this paper, we consider a linear Korteweg-de Vries equation posed in a bounded interval and study the time dependency with respect to the interval length and the transport coefficient, for which the uniform null controllability holds as the dispersion coefficient goes to zero. We consider two cases of boundary controls. First, only one control on the left end of the interval, and then, two controls acting on the right. The strategy is based on the combination of an exponential dissipation inequality and suitable Carleman estimates for each case.

中文翻译：

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线性Korteweg-de Vries方程一致零可控性的显式时间

在本文中，我们考虑在有界区间内提出的线性 Korteweg-de Vries 方程，并研究区间长度和输运系数的时间依赖性，其中当色散系数趋于零时，均匀零可控性成立。我们考虑边界控制的两种情况。首先，只有一个控件位于间隔的左端，然后，两个控件作用于右侧。该策略基于指数耗散不等式和针对每种情况的适当卡尔曼估计的组合。