Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions  

作　　者：Jing ZHAO Chun Mei GAN Zhen Hai LIU 

机构地区：[1]School of Mathematics and Quantitative Economics,Guangxi University of Finance and Economics,Nanning 530003,P.R.China [2]Guangxi Colleges and Universities Key Laboratory of Optimization Control and Engineering Calculation,Guangxi Minzu University,Nanning 530006,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第4期1143-1160,共18页数学学报（英文版）

基　　金：NSF of Guangxi(Grant No.2023GXNSFAA026085);Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.AD23023001);NNSF of China Grant Nos.12071413,12111530282 the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH;the Innovation Project of Guangxi University for Nationalities(Grant No.gxun-chxps202072)。

摘　　要：The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).

关 键 词：Differential parabolic hemivariational inequality Clarke subdifferential hyperbolicparabolic system parabolic-parabolic system existence result 

分 类 号：O178[理学—数学]