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.

Accepted:

DOI: 10.1051/cocv/2016012

Keywords: Controllablility, shape-dependent operator, shape optimization, shape derivative, partial differential equation, inverse problem

^{1}; Pinnau, R.

^{2}; Feßler, R.

^{1}

@article{COCV_2017__23_3_751_0, 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}, number = {3}, year = {2017}, doi = {10.1051/cocv/2016012}, mrnumber = {3660447}, zbl = {1365.93044}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016012/} }

TY - JOUR AU - Leithäuser, C. AU - Pinnau, R. AU - Feßler, R. TI - Approximate controllability of linearized shape-dependent operators for flow problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 751 EP - 771 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016012/ DO - 10.1051/cocv/2016012 LA - en ID - COCV_2017__23_3_751_0 ER -

%0 Journal Article %A Leithäuser, C. %A Pinnau, R. %A Feßler, R. %T Approximate controllability of linearized shape-dependent operators for flow problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 751-771 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016012/ %R 10.1051/cocv/2016012 %G en %F COCV_2017__23_3_751_0

Leithäuser, C.; Pinnau, R.; Feßler, R. Approximate controllability of linearized shape-dependent operators for flow problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 3, pp. 751-771. doi : 10.1051/cocv/2016012. http://archive.numdam.org/articles/10.1051/cocv/2016012/

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