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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 7.1

Time for local controllability of a 1-D

tank containing a fluid modeled by the

shallow water equations

Jean-Michel Coron

Université Paris-Sud

Département de Mathematique

Bâtiment 425

91405 Orsay

France

Jean-Michel.Coron@math.u-psud.fr

1 DESCRIPTION OF THE PROBLEM

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to one-dimensional horizontal moves. We assume that the horizontal acceleration of the tank is small compared to the gravity constant and that the height of the fluid is small compared to the length of the tank. This motivates the use of the Saint-Venant equations [5] (also called shallow water equations) to describe the motion of the fluid; see, e.g.,

[2, Sec. 4.2]. After ...

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