首页|A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

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In this paper,we study a generalized quasi-variational inequality(GQVI for short)with two multivalued operators and two bifunctions in a Banach space setting.A coupling of the Tychonov fixed point principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existence theorem for the GQVI.We also study a nonlinear optimal control problem driven by the GQVI and give sufficient conditions ensuring the existence of an optimal control.Finally,we illustrate the applicability of the theoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone and multivalued slip boundary condition(i.e.,a generalized friction constitutive law),a generalized leak boundary condition,a unilateral contact condition of Signorini's type and an implicit obstacle effect,in which the multivalued slip boundary condition is described by the generalized Clarke subgradient,and the leak boundary condition is formulated by the convex subdifferential operator for a convex superpotential.

generalized quasi-variational inequalityexistence theoremoptimal controlKakutani-Ky Fan theoremOseen problemnon-Newtonian fluidnonmonotone slip boundary condition

Shengda Zeng、Akhtar A.Khan、Stanis?aw Migórski

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Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Yulin 537000,China

Faculty of Mathematics and Computer Science,Jagiellonian University in Kraków,Kraków 30348,Poland

Center for Applied and Computational Mathematics,School of Mathematical Sciences,Rochester Institute of Technology,Rochester,NY 14623,USA

College of Sciences,Beibu Gulf University,Qinzhou 535000,China

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Guangxi Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaHorizon 2020 of the European UnionNational Science Center of PolandNational Science Foundation of USANational Science Center of PolandMinistry of Science and Higher Education of PolandMinistry of Science and Higher Education of Poland

2021GXNSFFA19600412001478823731 CONMECH2017/25/N/ST1/00611DMS 17200672021/41/B/ST1/016364004/GGPJII/H2020/2018/0440328/PnH2/2019

2024

10.1007/s11425-022-2069-0

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(2)
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