A GENERALIZED PENALTY METHOD FOR DIFFERENTIAL VARIATIONAL-HEMIVARIATIONAL INEQUALITIES  

作　　者：Liang LU Lijie LI Mircea SOFONEA 卢亮;李丽洁;Mircea SOFONEA(Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing,Guangxi University of Finance and Economics,Nanning 530003,China;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Yulin 537000,China;Laboratoire de Mathématiques et Physique,Universitéde Perpignan Via Domitia,52 Avenue Paul Alduy,66860 Perpignan,France)

机构地区：[1]Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing,Guangxi University of Finance and Economics,Nanning 530003,China [2]Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Yulin 537000,China [3]Laboratoire de Mathématiques et Physique,Universitéde Perpignan Via Domitia,52 Avenue Paul Alduy,66860 Perpignan,France

出　　处：《Acta Mathematica Scientia》2022年第1期247-264,共18页数学物理学报（B辑英文版）

基　　金：supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement(823731CONMECH);supported by National Natural Science Foundation of China(11671101),supported by National Natural Science Foundation of China(11961074);Guangxi Natural Science Foundation(2021GXNSFAA075022);Project of Guangxi Education Department(2020KY16017);Yulin normal university of scientific research fund for high-level talents(G2019ZK39,G2021ZK06)。

摘　　要：We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.

关 键 词：differential variational-hemivariational inequality generalized penalty method Mosco convergence viscoelastic rod unilateral constraint 

分 类 号：O178[理学—数学]