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Controllability and stabilization of gravity-capillary surface water waves in a basin

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It is dedicated to Professor Goong Chen on the occasion of his 70th birthday

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  • The paper concerns the controllability and stabilization of surface water waves in a two-dimensional rectangular basin under the forces of gravity and surface tension. The surface waves are generated by a wave-maker placed at the left side-boundary and it is physical relevant to see whether the surface waves are controllable or can be stabilized using appropriate motion of the wave-maker. Due to the surface tension, an edge condition must be imposed at the contact point between the free surface and a solid boundary. Two types of wave-makers are considered: "flexible" or "rigid". It is shown that the surface waves are approximately controllable, but not exactly controllable, for both "flexible" and "rigid" wave-makers. In addition, under a static feedback to control a "rigid" wave-maker, the strong stability of feedback control system is obtained.


    Correction: The page numbers on each page of the PDF file have been corrected. We apologize for any inconvenience this may cause.

    Mathematics Subject Classification: Primary: 76B15, 76B45; Secondary: 93C20.


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