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Convergence Results for Elliptic Variational-Hemivariational Inequalities.
- Source :
-
Advances in Nonlinear Analysis . 2021, Vol. 10 Issue 1, p2-23. 22p. - Publication Year :
- 2021
-
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 {𝓟n} 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]
- Subjects :
- *NONLINEAR operators
*BANACH spaces
*MATHEMATICAL models
Subjects
Details
- Language :
- English
- ISSN :
- 21919496
- Volume :
- 10
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 149124300
- Full Text :
- https://doi.org/10.1515/anona-2020-0107