广义余弦函数及一类二阶抽象柯西问题研究  

Generalized cosine operator function and the well-posedness of abstract Cauchy problem

作　　者：仓定帮 李庆庆 隋丽丽 CANG Dingbang;LI Qingqing;SUI Lili(School of Science, North China Institute of Science and Technology, Sanhe, Hebei 201601,China)

机构地区：[1]华北科技学院理学院,河北三河065201

出　　处：《华中师范大学学报（自然科学版）》2020年第3期339-344,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11702094);中央高校基本科研业务费项目(3142016011);华北科技学院创新团队项目(3142018059);河北省数据科学重点实验室项目(HBSJQ0707)。

摘　　要：首先基于广义二阶单参数分布系统的求解问题提出了广义余弦函数的概念;其次利用Laplace变换等工具,系统地刻画了广义余弦函数的性质;接着在给出广义余弦函数生成定理的基础上,对其逼近、扰动及遍历问题进行了分析;最后利用广义余弦函数工具对一类二阶抽象柯西问题的适定性进行了研究.First,by solving the problem of so called generalized second order singular distributed parameter system,the defifinition of generalized cosine operator function was introduced,and some basic properties of the generalized cosine operator function were characterized.Then the generation theory,approximation and perturbation theory and ergodic theory were also studied.Lastly,the well-posedness problem of generalized second order Cauchy problem was investigated.

关 键 词：广义余弦函数 柯西问题 逼近和扰动 遍历定理 适定性 

分 类 号：O152.7[理学—数学]