Download or read book Stabilization of the Systems Describing Water Waves and Their Interaction with a Floating Object written by Pei Su and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to studying the controllability and stabilizability properties of the control model coming from water waves problem and floating body system in a bounded domain. The equations used for the water waves system in this work is a fully linear and fully dispersive version of the Zakharov-Craig-Sulem formulation. The floating body system here is described by the nonlinear shallow water equations.The first part of this thesis aims to study the stability of a class of skew-adjoint control systems. This is motivated by the control problem of a linear water waves system. With the assumptions on the spectrum of the evolution operators involved in the control system, we obtain an explicit non-uniform decay rate of the energy of this system, provided that the initial data is smooth.We consider in the second part the small-amplitude water waves system in a rectangular domain, where the control acts on one lateral boundary, by imposing the velocity of the water. We first study the well-posedness of the whole system, which is addressed by formulating the equations as an abstract linear control system. Afterwards, we obtain the decay rate of the energy by using the general results in the first part. Next we study the asymptotic behaviour of the solution in the shallow water regime. It turns out the water waves system with boundary control converges to the waves equation in 1D with Neumann boundary control, when taking the shallowness limit.In the last part, we are interested in a rigid object floating in a bounded water tank. The object only moves in the vertical direction and the control is a vertical force imposed from the bottom of the object. We derive the nonlinear equations for this system and study the reachability and stabilizability of the linearized equations in various cases.