Geodesic
Approximate controllability of linearized shape-dependent operators for flow problems
Leithäuser, C.1 ; Pinnau, R.2 ; Feßler, R.1
1 Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.
2 TU Kaiserslautern, Department of Mathematics, Gottlieb-Daimler-Straße, 67663 Kaiserslautern, Germany.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 751-771

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We study the controllability of linearized shape-dependent operators for flow problems. The first operator is a mapping from the shape of the computational domain to the tangential wall velocity of the potential flow problem and the second operator maps to the wall shear stress of the Stokes problem. We derive linearizations of these operators, provide their well-posedness and finally show approximate controllability. The controllability of the linearization shows in what directions the observable can be changed by applying infinitesimal shape deformations.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016012
Classification : 93B05, 49Q10, 76B75, 35Q35, 35R30
Keywords: Controllablility, shape-dependent operator, shape optimization, shape derivative, partial differential equation, inverse problem

Leithäuser, C. 1 ; Pinnau, R. 2 ; Feßler, R. 1

1 Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.
2 TU Kaiserslautern, Department of Mathematics, Gottlieb-Daimler-Straße, 67663 Kaiserslautern, Germany. 
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     author = {Leith\"auser, C. and Pinnau, R. and Fe{\ss}ler, R.},
     title = {Approximate controllability of linearized shape-dependent operators for flow problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {751--771},
     publisher = {EDP-Sciences},
     volume = {23},
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     year = {2017},
     doi = {10.1051/cocv/2016012},
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     zbl = {1365.93044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016012/}
}
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Leithäuser, C.; Pinnau, R.; Feßler, R. Approximate controllability of linearized shape-dependent operators for flow problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 751-771. doi: 10.1051/cocv/2016012

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