具有时间依赖的时滞半线性二阶发展方程的能控性和适定性  

Controllability and well posedness for second order evolution differential equations

作　　者：施翠云 宾茂君 SHI Cui-yun;BIN Mao-jun(Guilin University of Technology at Nanning,Nanning 530001,Guangxi,China;Center for Applied Mathematics of Guangxi,Yulin Normal University,Yulin 537000,Guangxi,China)

机构地区：[1]桂林理工大学南宁分校基础学科部,广西南宁530001 [2]玉林师范学院广西应用数学中心,广西玉林537000

出　　处：《西北师范大学学报（自然科学版）》2024年第2期14-20,共7页Journal of Northwest Normal University(Natural Science)

基　　金：广西壮族自治区自然科学基金资助项目(2021GXNSFAA220130,2022GXNSFAA035617);广西高校中青年教师科研基础能力提升项目(2024KY0594,2023KY0599,2022KY0582)。

摘　　要：考虑状态依赖时滞的二阶发展微分方程的能控性和适定性.首先,利用不动点定理证明状态依赖时滞的二阶发展微分方程的可控性;其次,在适当条件下证明状态依赖时滞的二阶发展微分方程是适定的;最后,通过实例验证主要结果.This paper considers the controllability and well posedness of second order evolution differential equations with state dependent delay.Firstly,the controllability is proved for second order evolution differential equations with state dependent delay by using the fixed point theorem;Secondly,it is proved that the developed differential equation are well posed under appropriate conditions.In the end,an example is provided to represent the theory.

关 键 词：时滞 抽象微分方程 二阶发展方程 能控性 适定性 

分 类 号：O175.15[理学—数学]