Abstract

In this paper, we consider the problem of exact boundary controllability of a linear Korteweg-de Vries (KdV) equation in a bounded domain when the condition for the control is the difference between the derivative of the solution in the left and right endpoint. We prove the existence of a countable set of critical lengths out of which we have the exact controllability. In the second part of this paper, we study the behavior of the optimal control and how the cost of controllability evolves as the dispersive term brought to zero.

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