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Existence and Convergence Results for an Elastic Frictional Contact Problem with Nonmonotone Subdifferential Boundary Conditions

Authors
  • Liu, Yongjian1
  • Migórski, Stanisław2, 3
  • Nguyen, Van Thien4
  • Zeng, Shengda1, 3
  • 1 Yulin Normal University, Yulin, 537000, China , Yulin (China)
  • 2 Chengdu University of Information Technology, Chengdu, 610225, China , Chengdu (China)
  • 3 Chair of Optimization and Control, ul. Lojasiewicza 6, Krakow, 30348, Poland , Krakow (Poland)
  • 4 FPT University, Education Zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam , Hanoi (Vietnam)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 01, 2021
Volume
41
Issue
4
Pages
1151–1168
Identifiers
DOI: 10.1007/s10473-021-0409-5
Source
Springer Nature
Keywords
License
Yellow

Abstract

The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumptions, we deliver the weak formulation of the contact model, which is an elliptic system with Lagrange multipliers, and which consists of a hemivariational inequality and a variational inequality. Then, we prove the solvability of the contact problem. Finally, employing the notion of H-convergence of nonlinear elasticity tensors, we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator, body forces, and surface tractions.

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