Boundary feedback stabilization of hydraulic jumps
Résumé
In an open channel, a hydraulic jump is an abrupt transition between a torrential (super-critical) flow and a fluvial (subcritical) flow. In this article hydraulic jumps are represented by discontinuous shock solutions of hyperbolic Saint-Venant equations. Using a Lyapunov approach, we prove that we can stabilize the state of the system in $H^2$-norm as well as the hydraulic jump location, with simple feedback boundary controls and an arbitrary decay rate, by appropriately choosing the gains of the feedback boundary controls.
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