# Asymptotic behaviour of a linearized water waves system in a rectangle

@inproceedings{Su2021AsymptoticBO, title={Asymptotic behaviour of a linearized water waves system in a rectangle}, author={Pei-lan Su}, year={2021} }

We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a scalar input function u. The state z of the system consists of two functions: the water level ζ along the top boundary, and its time derivative ∂ζ ∂t . We prove that the solution of the water waves system…

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