History-dependent differential variational-hemivariational inequalities with applications to contact mechanics

Zhenhai Liu; Van Thien Nguyen; Jen-Chih Yao; Shengda Zeng

doi:10.3934/eect.2020044

Article Contents

2020, Volume 9, Issue 4: 1073-1087. Doi: 10.3934/eect.2020044

This issue Previous Article Differential inclusion problems with convolution and discontinuous nonlinearities Next Article Fully history-dependent evolution hemivariational inequalities with constraints

History-dependent differential variational-hemivariational inequalities with applications to contact mechanics

1.
College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi, China
2.
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization, and Big Data Processing, Yulin Normal University, Yulin 537000, China
3.
Departement of Mathematics, FPT University, Education zone, Hoa Lac high tech park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam
4.
Center for General Education, China Medical University, Taichung, Taiwan
5.
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348 Krakow, Poland

^* Corresponding author: Shengda Zeng
^* Corresponding author: Shengda Zeng

Dedicated to Professor Meir Shillor on the occasion of his 70th birthday.

Received: September 2019

Early access: March 2020

Published: December 2020

This project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 – CONMECH. It is also supported by the National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611, NNSF of China Grant No. 11671101, NSF of Guangxi Grant No. 2018GXNSFDA138002, and International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0

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Abstract

The primary objective of this paper is to explore a complicated differential variational-hemivariational inequality involving a history-dependent operator in Banach spaces. A well-posedness result for the inequality, including the existence, uniqueness, and continuous dependence on the initial data of the solution is established by using a fixed point principle for history-dependent operators. Moreover, to illustrate the applicability of the theoretical results, an elastic contact problem with wear and long time dependent effort is explored.

Keywords:

Differential variational-hemivariational inequality,
well-posedness,
history-dependent operator,
compliance,
wear.

Mathematics Subject Classification: Primary: 35L86, 35L87; Secondary: 74Hxx, 74M15.

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References

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