Banach空间中微分变分不等式系统的Bang-Bang准则  

On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces

作　　者：施翠云 宾茂君 Shi Cuiyun;Bin Maojun(Guilin University of Technology at Nanning,Nanning 530001;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Guangxi Yulin 537000;School of Mathematics and Statistics,Yulin Normal University,Guangxi Yulin 537000)

机构地区：[1]桂林理工大学南宁分校,南宁530001 [2]玉林师范学院广西高校复杂系统优化与大数据处理重点实验室,广西玉林537000 [3]玉林师范学院数学与统计学院,广西玉林537000

出　　处：《数学物理学报（A辑）》2022年第6期1653-1670,共18页Acta Mathematica Scientia

基　　金：广西自然科学基金(2020GXNSFAA159152,2020GXNSFBA297142,2021GXNSFAA220130,2022GXNSFAA035617)。

摘　　要：该文将讨论一类由半线性发展方程和广义变分不等式所组成的微分变分不等式系统.首先,考虑广义变分不等式解集的性质.其次,通过利用不动点定理和半群理论证明了微分变分不等式系统解的存在性.另外,通过运用稠定性结果证明了微分变分不等式系统的Bang-Bang准则.同时,运用一个障碍型抛物-椭圆系统来检验该文的主要结果.In this paper,we discuss a class of differential variational inequalities systems,which are obtained by semilinear evolution equations and generalized variational inequalities.At first,we consider the properties of solution set for generalized variational inequalities.Secondly,the existence results are shown by fixed point method for semilinear differential variational inequality.Our approaches are based on semigroup theory and fixed point theorem.Moreover,by using the density results,the nonlinear and infinite dimensional versions of the"bang-bang"principle for differential variational inequalities systems is derived.Also,an obstacle parabolic-elliptic system is given to illustrate the application of the obtained theory.

关 键 词：微分变分不等式 Bang-Bang准则 稠定性 KKM映射. 

分 类 号：O176.3[理学—数学]