1. Convergence Results for Elliptic Variational-Hemivariational Inequalities.
- Author
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Cai, Dong-ling, Sofonea, Mircea, and Xiao, Yi-bin
- Subjects
NONLINEAR operators ,BANACH spaces ,MATHEMATICAL models - 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 𝓟n 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 𝓟n , 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 𝓟n . 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. [ABSTRACT FROM AUTHOR]- Published
- 2021
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