Geodesic
Stability and Boundary Controllability of a Linearized Model of Flow in an Elastic Tube
Peralta, Gilbert1, 2 ; Propst, Georg2
1 Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, 2600 Baguio City, Philippines.
2 Institut für Mathematik und Wissenschaftliches Rechnen, NAWI Graz, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 583-601

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We consider a model describing the flow of a fluid inside an elastic tube that is connected to two tanks. We study the linearized system through semigroup theory. Controlling the pressures in the tanks renders a hyperbolic PDE with boundary control. The linearization induces a one-dimensional linear manifold of equilibria; when those are factored out, the corresponding semigroup is exponentially stable. The location of the eigenvalues in dependence on the viscosity is discussed. Exact boundary controllability of the system is achieved by the Riesz basis approach including generalized eigenvectors. A minimal time for controllability is given. The corresponding result for internal distributed control is stated.

Reçu le :
DOI : 10.1051/cocv/2014039
Classification : 35L50, 47D03, 93C20
Keywords: Flow in elastic tube, semigroup, exponential stability, boundary control system, exact controllability, Riesz basis

Peralta, Gilbert 1, 2 ; Propst, Georg 2

1 Department of Mathematics and Computer Science, University of the Philippines Baguio, Governor Pack Road, 2600 Baguio City, Philippines.
2 Institut für Mathematik und Wissenschaftliches Rechnen, NAWI Graz, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria. 
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     title = {Stability and {Boundary} {Controllability} of a {Linearized} {Model} of {Flow} in an {Elastic} {Tube}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {583--601},
     publisher = {EDP-Sciences},
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     year = {2015},
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     zbl = {1330.35033},
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Peralta, Gilbert; Propst, Georg. Stability and Boundary Controllability of a Linearized Model of Flow in an Elastic Tube. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 583-601. doi: 10.1051/cocv/2014039

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