Strong stabilization of small water waves in a pool

Pei Su, Marius Tucsnak, George Weiss

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


This 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 function u, times a function h of the position along the active boundary. The state 2: of the system is a vector with two components: one is the water level £ along the top boundary, and the other is its time derivative We prove that for suitable functions ht there exists a bounded feedback functional F such that the feedback u = Fz leads 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 4-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).

Original languageEnglish
Pages (from-to)378-383
Number of pages6
Issue number9
StatePublished - 1 Jun 2021
Event24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020 - Cambridge, United Kingdom
Duration: 23 Aug 202127 Aug 2021


  • Collocated actuators and sensors
  • Dirichlet to neumann map
  • Linearized water waves equation
  • Neumann to neumann map
  • Strong stabilization


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