Abstract

We focus on the linear Kawahara equation in a bounded domain, employing two boundary controls. The controllability of this system has been previously demonstrated over the past decade using the Hilbert uniqueness method, which involves proving an observability inequality, in general, shown via Carleman estimates. Here, we extend this understanding by achieving exact controllability within a space of analytic functions, employing the flatness approach, which is a new approach for higher-order dispersive systems. We also provide a class of reachable states (taking $0$ as initial data) which are holomorphic in some disk around $0$.

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