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.
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)
出处
《数学物理学报（A辑）》
CSCD
北大核心
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)。
作者简介
通讯作者:宾茂君,E-mail:bmj1999@163.com。
