Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F16%3A00000277" target="_blank" >RIV/46747885:24220/16:00000277 - isvavai.cz</a>

Výsledek na webu

<a href="http://onlinelibrary.wiley.com/doi/10.1002/zamm.201500117/abstract" target="_blank" >http://onlinelibrary.wiley.com/doi/10.1002/zamm.201500117/abstract</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/zamm.201500117" target="_blank" >10.1002/zamm.201500117</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

Popis výsledku v původním jazyce

We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [8], in the present paper the threshold value may depend on the velocity field. Besides the usual velocity-pressure formulation, we introduce an alternative formulation with three Lagrange multipliers which allows a more flexible treatment of the impermeability condition as well as optimum design problems with cost functions depending on the shear and/or normal stress. Our main goal is to determine under which conditions concerning smoothness of the boundary of Ω, solutions to the Stokes system 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.

Název v anglickém jazyce

Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

Popis výsledku anglicky

We study the Stokes problem in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [8], in the present paper the threshold value may depend on the velocity field. Besides the usual velocity-pressure formulation, we introduce an alternative formulation with three Lagrange multipliers which allows a more flexible treatment of the impermeability condition as well as optimum design problems with cost functions depending on the shear and/or normal stress. Our main goal is to determine under which conditions concerning smoothness of the boundary of Ω, solutions to the Stokes system 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

ISSN

1521-4001

e-ISSN

—

Svazek periodika

96

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

12

Strana od-do

1049-1060

Kód UT WoS článku

000385670000003

EID výsledku v databázi Scopus

2-s2.0-84985916233