A Class of Variational-Hemivariational Inequalities for Bingham Type Fluids

被引：19

作者：

Migorski, Stanislaw ^{[1
,2
]}

Dudek, Sylwia ^{[3
]}

机构：

[1] Chengdu Univ Informat Technol, Coll Appl Math, Chengdu 610225, Sichuan, Peoples R China

[2] Jagiellonian Univ Krakow, Chair Optimizat & Control, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

[3] Krakow Univ Technol, Fac Comp Sci & Telecommun, Dept Appl Math, Ul Warszawska 24, PL-31155 Krakow, Poland

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2022年 / 85卷 / 02期

基金：

欧盟地平线“2020”;

关键词：

Bingham type fluid; Variational-hemivariational inequality; Generalized subgradient; Leak and slip condition; Optimal control; FINITE-ELEMENT APPROXIMATION; GENERALIZED NEWTONIAN FLUID; BOUNDARY-CONDITIONS; STOKES EQUATIONS; WEAK SOLUTIONS; ERROR-BOUNDS; EXISTENCE; REGULARITY; FLOWS; MODEL;

D O I：

10.1007/s00245-022-09855-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate a new class of elliptic variational-hemivariational inequalities without the relaxed monotonicity condition of the generalized subgradient. The inequality describes the mathematical model of the steady state flow of incompressible fluid of Bingham type in a bounded domain. The boundary condition represents a generalization of the no leak condition, and a multivalued and nonmonotone version of a nonlinear Navier-Fujita frictional slip condition. The analysis provides results on existence of solution to a variational-hemivariational inequality, continuous dependence of the solution on the data, existence of solutions to optimal control problems, and the dependence of the solution on the yield limit. The proofs profit from results of nonsmooth analysis and the theory of multivalued pseudomontone operators.

引用

页数：29

共 36 条

[1]

[Anonymous], 2012, Springer Monographs in Mathematics

[2]

Bao WZ, 1998, RAIRO-MATH MODEL NUM, V32, P843

[3] On Flows of Bingham-Type Fluids with Threshold Slippage [J].