Abstract
In this Note we introduce the asymptotic controllability and the asymptotic null controllability for 1- D linear hyperbolic systems under the lack of boundary controls. We claim that they are equivalent, respectively, to the strong observability and the weak observability for the dual system. An example of 4 × 4 hyperbolic system with only one boundary control is shown to be asymptotically controllable but not exactly controllable.
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