EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

doi:10.1007/s10473-021-0409-5

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1151-1168.doi: 10.1007/s10473-021-0409-5

EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

刘永建¹, Stanis law MIGORSKI², Van Thien NGUYEN³, 曾生达⁴

1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China;
2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China Jagiellonian University in Krakow, Chair of Optimization and Control, ul. Lojasiewicza 6, 30348 Krakow, Poland;
3. Departement of Mathematics, FPT University, Education Zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam;
4. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China Jagiellonian University in Krakow, Chair of Optimization and Control, ul. Lojasiewicza 6, 30348 Krakow, Poland

收稿日期:2020-03-03 修回日期:2020-10-26 出版日期:2021-08-25 发布日期:2021-09-01
通讯作者: Shengda ZENG E-mail:zengshengda@163.com
作者简介:Yongjian LIU,E-mail:liuyongjianmaths@126.com;Stanis law MIGORSKI,E-mail:Thiennv15@fe.edu.vn;Shengda ZENG,E-mail:zengshengda@163.com
基金资助:
The project supported by the NNSF of China Grants Nos. 12001478, 12026255, 12026256 and 11961074, H2020-MSCA-RISE-2018 Research and Innovation Staff Exchange Scheme Fellowship within the Project No. 823731 CONMECH, and National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611. It is also supported by the Startup Project of Doctor Scientific Research of Yulin Normal University No. G2020ZK07, Natural Science Foundation of Guangxi Province Grants Nos. 2018GXNSFDA281028 and 2020GXNSFBA297137, and the High Level Innovation Team Program from Guangxi Higher Education Institutions of China (Document no.[2018] 35).

EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

Yongjian LIU¹, Stanis law MIGORSKI², Van Thien NGUYEN³, Shengda ZENG⁴

1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China;
2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China Jagiellonian University in Krakow, Chair of Optimization and Control, ul. Lojasiewicza 6, 30348 Krakow, Poland;
3. Departement of Mathematics, FPT University, Education Zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam;
4. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China Jagiellonian University in Krakow, Chair of Optimization and Control, ul. Lojasiewicza 6, 30348 Krakow, Poland

Received:2020-03-03 Revised:2020-10-26 Online:2021-08-25 Published:2021-09-01
Contact: Shengda ZENG E-mail:zengshengda@163.com
Supported by:
The project supported by the NNSF of China Grants Nos. 12001478, 12026255, 12026256 and 11961074, H2020-MSCA-RISE-2018 Research and Innovation Staff Exchange Scheme Fellowship within the Project No. 823731 CONMECH, and National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611. It is also supported by the Startup Project of Doctor Scientific Research of Yulin Normal University No. G2020ZK07, Natural Science Foundation of Guangxi Province Grants Nos. 2018GXNSFDA281028 and 2020GXNSFBA297137, and the High Level Innovation Team Program from Guangxi Higher Education Institutions of China (Document no.[2018] 35).

摘要/Abstract

摘要： 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.

关键词: Mixed variational-hemivariational inequality, H-convergence, homogenization, Clarke subgradient, Lagrange multiplier, elasticity operator

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.

Key words: Mixed variational-hemivariational inequality, H-convergence, homogenization, Clarke subgradient, Lagrange multiplier, elasticity operator

中图分类号:

35L15

刘永建, Stanis law MIGORSKI, Van Thien NGUYEN, 曾生达. EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2021, 41(4): 1151-1168.

Yongjian LIU, Stanis law MIGORSKI, Van Thien NGUYEN, Shengda ZENG. EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1151-1168.

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EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

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