降阶型热波方程解的存在性和唯一性  

Existence and Uniqueness of the Solution to the Hot-Wave Equation by the Order Reduction

作　　者：金雪莲[1] 张思佳[2] JIN Xue-lian;ZHANG Si-jia(College of Science,Liaoning University of Technology,Jinzhou 121001,China;College of Science,College of Bohai,Jinzhou 121013,China)

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001 [2]渤海大学理学院,辽宁锦州121013

出　　处：《辽宁工业大学学报（自然科学版）》2021年第3期206-210,共5页Journal of Liaoning University of Technology(Natural Science Edition)

基　　金：辽宁省教育厅科学研究经费项目(JJL201915408)。

摘　　要：为了后续对热波方程引入李雅普诺夫函数证明连续及离散系统的一致稳定性提供必要的前提和理论基础,首先将热波方程进行降阶处理,然后在Hibert空间上介绍了连续系统的状态空间以及定义在其上的内积,最后通过算子半群理论证明降阶后的方程解的存在性和唯一性。In order to provide the necessary premise and theoretical basis for the subsequent introduction to Lyapunov function to prove the uniform exponential stability of continuous and discrete systems,the order of hot-wave equation is reduced.Then,the state space of continuous systems and inner product of continuous systems are introduced in Hilbert space.Finally,the existence and uniqueness of the solution to the equation are proved by the theory of operator semigroup.

关 键 词：HIBERT空间 热波方程 动态边界条件 

分 类 号：O231[理学—运筹学与控制论]