星形集约束微分变分不等式解的存在性  

The Existence of Solutions to Differential Variational Inequalities Constraints on Star-shaped Sets

作　　者：卢亮 郭秀凤 LU Liang;GUO Xiufeng(School of Information and Statistics,Guangxi Key Laboratory of Cross-border E-commerce Intelligent Information Processing,Guangxi University of Finance and Economics,Nanning 530003,China)

机构地区：[1]广西财经学院信息与统计学院,广西跨境电商智能信息处理重点实验室(广西财经学院),南宁530003

出　　处：《应用数学学报》2021年第5期603-618,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11671101);广西自然科学基金(2021GXNSFAA075022);广西财经学院创新团队支持计划经费;广西高校中青年教师科研基础能力提升项目(2020KY16017)资助。

摘　　要：由微分方程和变分不等式构成的微分变分不等式是非线性分析及其应用领域中的一类非常重要的问题,吸引了不少学者的极大关注和探索.本文研究一类具有非凸约束的微分变分不等式新问题的解的存在性.该类问题中的变分不等式的约束集是关于某一球的星形集,使得可以利用距离函数的广义Clarke次微分的不连续性质.我们通过多值伪单调算子的满射定理,H-半变分不等式逼近和参数不需要趋于零的罚方法证明解的存在性,并举例说明主要结果在具有非凸约束的抛物型初值问题中的应用.The differential variational inequality composed of differential equation and variational inequality is a very important problem in the field of nonlinear analysis and its application.Recently,differential variational inequality has attracted the great attention and exploration of many scholars.In this paper,we study the existence of solutions to a new class of differential variational inequalities with nonconvex constraint set,but the constraint set of the variational inequality for this kind of problems is star-shaped with respect to a certain ball.This allows one to use a discontinuity property of the generalized Clarke subdifferential of the distance function.Then the existence of solutions to differential variational inequalities are obtained by applying a surjectivity theorem for multivalued pseudomonotone operators,a hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero.Finally,as samples of applications,we consider a parabolic initial-boundary value problem with nonconvex constraint and illustrate the application of the main results.

关 键 词：微分变分不等式 解的存在性 满射定理 H-半变分不等式 罚方法 

分 类 号：O175[理学—数学]