Volume 23, Number 3, July-September 2017
|Page(s)||751 - 771|
|Published online||31 January 2017|
Approximate controllability of linearized shape-dependent operators for flow problems
1 Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.
2 TU Kaiserslautern, Department of Mathematics, Gottlieb-Daimler-Straße, 67663 Kaiserslautern, Germany.
3 Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.
Received: 14 October 2014
Revised: 27 October 2015
Accepted: 18 February 2016
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.
Mathematics Subject Classification: 93B05 / 49Q10 / 76B75 / 35Q35 / 35R30
Key words: Controllablility / shape-dependent operator / shape optimization / shape derivative / partial differential equation / inverse problem
© EDP Sciences, SMAI 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.