Shape optimization for Stokes problem with threshold slip

0436795 - MÚ 2015 RIV CZ eng J - Journal Article
Haslinger, J. - Stebel, Jan - Taoufik, S.
Shape optimization for Stokes problem with threshold slip.
Applications of Mathematics. Roč. 59, č. 6 (2014), s. 631-652. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GA201/09/0917; GA ČR(CZ) GAP201/12/0671
Institutional support: RVO:67985840
Keywords : Stokes problem * friction boundary condition * shape optimization
Subject RIV: BA - General Mathematics
Impact factor: 0.400, year: 2014
http://link.springer.com/article/10.1007%2Fs10492-014-0077-z

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.
Permanent Link: http://hdl.handle.net/11104/0240457