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Shape optimization for Stokes problem with threshold slip
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SYSNO ASEP 0436795 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Shape optimization for Stokes problem with threshold slip Author(s) Haslinger, J. (CZ)
Stebel, Jan (MU-W) RID, ORCID, SAI
Taoufik, S. (FR)Source Title Applications of Mathematics. - : Springer - ISSN 0862-7940
Roč. 59, č. 6 (2014), s. 631-652Number of pages 22 s. Language eng - English Country CZ - Czech Republic Keywords Stokes problem ; friction boundary condition ; shape optimization Subject RIV BA - General Mathematics R&D Projects GA201/09/0917 GA ČR - Czech Science Foundation (CSF) GAP201/12/0671 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000345089100003 EID SCOPUS 84919918891 DOI 10.1007/s10492-014-0077-z Annotation We study the Stokes problems in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning the smoothness of Ω solutions to the Stokes system with the slip boundary conditions depend continuously on variations of Ω. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2015
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