Affiliation:
1. School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan, 611731 , PR China
2. University of Perpignan Via Domitia , 52 Avenue Paul Alduy, 66860 , Perpignan , France
Abstract
Abstract
We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟
n
} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟
n
is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter εn
. The unique solvability of 𝓟 and, for each n ∈ ℕ, the solvability of its perturbed version 𝓟
n
, are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem 𝓟 and, for each n ∈ ℕ, let un
be a solution of Problem 𝓟
n
. The main result of this paper states the strong convergence of un
→ u in X, as n → ∞. We show that the main result extends a number of results previously obtained in the study of Problem 𝓟. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations.
Reference37 articles.
1. D. L. Cai, M. Sofonea and Y. B. Xiao, Tykhonov well-posedness of a mixed variational problem, submitted.
2. F. H. Clarke, Optimization and Nonsmooth Analysis, Society for Industrial and Applied Mathematics, New York, 1983.
3. Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Theory, Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003.
4. Z. Denkowski, S. Migórski and N. S. Papageorgiou, An Introduction to Nonlinear Analysis: Applications, Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003.
5. F. Giannessi and A. Khan, Regularization of non-coercive quasi-variational inequalities, Control Cybernet. 29 (2000), 91–110.
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献