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2009, Volume 4, Issue 2: 177-187. Doi: 10.3934/nhm.2009.4.177
This issue Previous Article Preface Next Article Methods for the localization of a leak in open water channels

On Lyapunov stability of linearised Saint-Venant equations for a sloping channel

  • 1.

    Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve

  • 2.

    Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Institut Universitaire de France, 175, Rue du Chevaleret, 75013 Paris

  • 3.

    Centre de Robotique (CAOR), Ecole nationale supérieure des mines de Paris, 60, Boulevard Saint Michel, 75272 Paris Cedex 06

Received:  October 2008
Revised:  January 2009
Published:  June 2009
Abstract Related Papers Cited by
    Abstract
  • We address the issue of the exponential stability (in $L^2$-norm) of the classical solutions of the linearised Saint-Venant equations for a sloping channel. We give an explicit sufficient dissipative condition which guarantees the exponential stability under subcritical flow conditions without additional assumptions on the size of the bottom and friction slopes. The stability analysis relies on the same strict Lyapunov function as in our previous paper [5]. The special case of a single pool is first treated. Then, the analysis is extended to the case of the boundary feedback control of a general channel with a cascade of $n$ pools.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:
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