Convergence Results for Elliptic Variational-Hemivariational Inequalities

Advances in Nonlinear Analysis

article

Dong-ling Cai¹  Mircea Sofonea²  Yi-bin Xiao¹ 

[1] School of Mathematical Sciences, University of Electronic Science and Technology of China;University of Perpignan Via Domitia

关键词: variational-hemivariational inequality;    penalty operator;    Mosco convergence;    internal approximation;    Tykhonov well-posedness;    contact problem;   

DOI  :  10.1515/anona-2020-0107

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider an elliptic variational-hemivariational inequality ? 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 {? n } of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality ? n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter ε n . The unique solvability of ? and, for each n ∈ ℕ, the solvability of its perturbed version ? n , are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem ? and, for each n ∈ ℕ, let u n be a solution of Problem ? n . The main result of this paper states the strong convergence of u n → u in X , as n → ∞. We show that the main result extends a number of results previously obtained in the study of Problem ?. 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.

【 授权许可】

CC BY