Control of the surface of a fluid by a wavemaker

Lionel Rosier (1)

1 IECN - Institut Élie Cartan de Nancy

Mots clés: Control of the surface of water in a long canal by means of a wavemaker is considered. Canals with a moving boundary are simple devices used to study water waves. The fluid motion is simulated by the Korteweg-de Vries (KdV) equation in Lagrangian coordinates. The main result in this paper asserts that any (smooth) trajectory for the KdV equation may be (locally) reached in finite time. In particular; the KdV equation is locally null controllable by using a special quadratic boundary control. The proof is based on a Carleman estimate of solutions and some weighted inequalities. Global uncontrollability is also established.; the KdV equation is locally null controllable by using a special quadratic boundary control. The proof is based on a Carleman estimate of solutions and some weighted inequalities. Global uncontrollability is also established

Domaines: Equations aux dérivées partielles [math.AP]

Lionel Rosier. Control of the surface of a fluid by a wavemaker. ESAIM: Control, Optimisation and Calculus of Variations, 2004, 10 (3), pp.346-380. ⟨hal-00146833⟩