Time-dependent elliptic quasi-variational-hemivariational inequalities: well-posedness and application

Tie-jun Jiang, Dong-ling Cai, Yi-bin Xiao () and Stanisław Migórski
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Tie-jun Jiang: University of Electronic Science and Technology of China
Dong-ling Cai: University of Electronic Science and Technology of China
Yi-bin Xiao: University of Electronic Science and Technology of China
Stanisław Migórski: Jagiellonian University in Krakow, Chair of Optimization and Control

Journal of Global Optimization, 2024, vol. 88, issue 2, No 10, 509-530

Abstract: Abstract In this paper we investigate a class of time-dependent quasi-variational-hemivariational inequalities (TDQVHVIs) of elliptic type in a reflexive separable Banach space, which is characterized by a constraint set depending on a solution. The solvability of the TDQVHVIs is obtained by employing a measurable selection theorem for measurable set-valued mappings, while the uniqueness of solution to the TDQVHVIs is guaranteed by enhancing the assumptions on the data. Then, under additional hypotheses, we deliver a continuous dependence result when all the data are subjected to perturbations. Finally, the applicability of the abstract results is illustrated by a frictional elastic contact problem with locking materials for which the existence and stability of the weak solutions is proved.

Keywords: Quasi-variational-hemivariational inequality; Measurable selection; Solvability; Continuous dependence; Frictional contact problem; 28B20; 47J20; 49J27; 49J40; 74M15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01324-6

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