摘要：AbstractThis paper is about the strong stabilization of small amplitude gravity water waves in a vertical rectangle. The control imposes the horizontal acceleration of the water along one vertical boundary segment, as a multiple of a scalar input functionu,times a functionhof the position along the active boundary. The statezof the system is a vector with two components: one is the water levelζalong the top boundary and the other is its time derivative ζ. We prove that for suitable functionsh,there exists a bounded feedback functionalFsuch that the feedbacku=Fzleads to a strongly stable closed-loop system. Moreover, for initial states in the domain of the semigroup generator, the norm of the solution decays like (1 + t) − 1/6. Our approach uses careful estimates on certain partial Dirichlet to Neumann and Neumann to Neumann operators associated to the rectangular domain, as well as non-uniform stabilization results due to Chill, Paunonen, Seifert, Stahn and Tomilov (2019).
关键词：KeywordsLinearized water waves equationcollocated actuatorssensorsDirichlet to Neumann mapNeumann to Neumann mapstrong stabilization
