A Class of Multivalued Quasi-Variational Inequalities with Applications

被引：0
作者：
Stanislaw Migórski
Yunru Bai
Sylwia Dudek
机构：
[1] Chengdu University of Information Technology,College of Applied Mathematics
[2] Guangxi University of Science and Technology,School of Science
[3] Jagiellonian University,Chair of Optimization and Control
[4] Krakow University of Technology,Department of Applied Mathematics, Faculty of Computer Science and Telecommunications
来源：
Applied Mathematics & Optimization | 2023年 / 87卷
关键词：
Variational inequality; Hemivariational inequality; Kuratowski convergence; Mosco convergence; Fixed point; Nonsmooth contact problem; Clarke subgradient; P35J87; 49J40; 76A05; 76M30;
D O I：
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学科分类号：
摘要：
In this paper we deal with a class of nonlinear quasi-variational inequalities involving a set-valued map and a constraint set. First, we prove that the set of weak solutions of the inequality is nonempty, weakly compact and upper semicontinuous with respect to perturbations in the data. Then, the results are applied to a quasi variational-hemivariational inequality of elliptic kind. Finally, as an illustrative applications we examine a mathematical model of a nonsmooth static frictional unilateral contact problem for ideally locking materials in nonlinear elasticity.
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[1]  
Brézis H(1968)Equations et inéquations non linéaires dans les espaces vectoriels en dualité Ann. Inst. Fourier (Grenoble) 18 115-175
[2]  
Browder FE(1965)Nonlinear monotone operators and convex sets in Banach spaces Bull. Amer. Math. Soc. 71 780-785
[3]  
Browder F(1972)Nonlinear mappings of monotone type in Banach spaces J. Funct. Anal. 11 251-294
[4]  
Hess P(2022)Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems Inverse Probl. 38 28-211
[5]  
Cen JX(1986)On locking materials Acta Appl. Math. 6 185-1333
[6]  
Khan AA(2018)Evolutionary Oseen model for generalized Newtonian fluid with multivalued nonmonotone friction law J. Math. Fluid Mech. 20 1317-286
[7]  
Motreanu D(2019)Numerical analysis of hemivariational inequalities in contact mechanics Acta Numer. 28 175-3912
[8]  
Zeng SD(2014)A class of variational-hemivariational inequalities with applications to frictional contact problems SIAM J. Math. Anal. 46 3891-1161
[9]  
Demengel F(2015)Existence theorems for elliptic and evolutionary variational and quasi-variational inequalities J. Optim. Theory Appl. 167 1136-411
[10]  
Suquet P(2018)Inverse problems for quasi-variational inequalities J. Global Optim. 70 401-519
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