Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 513-554

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint-Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

DOI : 10.1051/cocv:2002050
Classification : 76B75, 93B05, 76B15, 35F30
Keywords: controllability, hyperbolic systems, shallow water 
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     author = {Coron, Jean-Michel},
     title = {Local controllability of a {1-D} tank containing a fluid modeled by the shallow water equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {513--554},
     year = {2002},
     publisher = {EDP Sciences},
     volume = {8},
     doi = {10.1051/cocv:2002050},
     mrnumber = {1932962},
     zbl = {1071.76012},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2002050/}
}
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Coron, Jean-Michel. Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 513-554. doi: 10.1051/cocv:2002050

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