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

Zhenhai Liu, ,College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi, China, Van Thien Nguyen, Jen-Chih Yao, Shengda Zeng, ,Guangxi Colleges and Universities Key Laboratory of Complex System Optimization, and Big Data Processing, Yulin Normal University, Yulin 537000, China, ,Departement of Mathematics, FPT University, Education zone, Hoa Lac high tech park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam, ,Center for General Education, China Medical University, Taichung, Taiwan, ,Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348 Krakow, Poland
2019 Evolution Equations and Control Theory  

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Dedicated to Professor Meir Shillor on the occasion of his 70th birthday. 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
more » ... rate the applicability of the theoretical results, an elastic contact problem with wear and long time dependent effort is explored.
doi:10.3934/eect.2020044 fatcat:bqbcekw7vzgbxoirysg7jhqzxi
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Zhenhai Liu, ,College of Sciences, Guangxi University for Nationalities, Nanning 530006, Guangxi, China, Van Thien Nguyen, Jen-Chih Yao, Shengda Zeng, ,Guangxi Colleges and Universities Key Laboratory of Complex System Optimization, and Big Data Processing, Yulin Normal University, Yulin 537000, China, ,Departement of Mathematics, FPT University, Education zone, Hoa Lac high tech park, Km29 Thang Long highway, Thach That ward, Hanoi, Vietnam, ,Center for General Education, China Medical University, Taichung, Taiwan, ,Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348 Krakow, Poland. "History-dependent differential variational-hemivariational inequalities with applications to contact mechanics." Evolution Equations and Control Theory 9.4 (2019) 0-0