Shape optimization for Stokes problem with threshold slip

Jaroslav Haslinger; Jan Stebel; Taoufik Sassi

Applications of Mathematics (2014)

  • Volume: 59, Issue: 6, page 631-652
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Haslinger, Jaroslav, Stebel, Jan, and Sassi, Taoufik. "Shape optimization for Stokes problem with threshold slip." Applications of Mathematics 59.6 (2014): 631-652. <http://eudml.org/doc/261981>.

@article{Haslinger2014,
abstract = {We study the Stokes problems in a bounded planar domain $\Omega $ 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 $\Omega $ solutions to the Stokes system with the slip boundary conditions depend continuously on variations of $\Omega $. 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.},
author = {Haslinger, Jaroslav, Stebel, Jan, Sassi, Taoufik},
journal = {Applications of Mathematics},
keywords = {Stokes problem; friction boundary condition; shape optimization; Stokes problem; friction boundary condition; shape optimization},
language = {eng},
number = {6},
pages = {631-652},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization for Stokes problem with threshold slip},
url = {http://eudml.org/doc/261981},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Stebel, Jan
AU - Sassi, Taoufik
TI - Shape optimization for Stokes problem with threshold slip
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 6
SP - 631
EP - 652
AB - We study the Stokes problems in a bounded planar domain $\Omega $ 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 $\Omega $ solutions to the Stokes system with the slip boundary conditions depend continuously on variations of $\Omega $. 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.
LA - eng
KW - Stokes problem; friction boundary condition; shape optimization; Stokes problem; friction boundary condition; shape optimization
UR - http://eudml.org/doc/261981
ER -

References

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