具有内部控制和边界观测具有时滞的单管热交换方程的指数稳定性

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具有内部控制和边界观测具有时滞的单管热交换方程的指数稳定性郑福¹, 聂坤¹, 郭宝珠²1. 渤海大学数理学院数学系, 锦州 121013;
2. 中国科学院系统科学与数学研究院, 北京 100190 Heat Exchanger Equation with Inner Control four and Boundary Observation with Delay ZHENG Fu¹, ZHANG Yang¹, GUO Baozhu²1. Department of Mathematics, Science College, Bohai University, Jinzhou 121013, China;
2. Academy of Mathematics and Systems Science, CAS, Beijing 100190, China

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摘要本文研究了具有时滞边界观测和内部控制的单管热交换方程的指数稳定性.首先，将闭环系统转换为合适状态空间上的抽象柯西问题.通过验证，闭环系统生成一个一致有界的C₀半群，意味着系统存在唯一解.其次，分析了系统的谱分布，通过某些预解集上的预解式估计得到生成半群的最终可微性和最终紧性，这意味着系统的谱确定增长假设成立.最后，给出了系统指数稳定性的一个充分条件，此充分条件与物理参数有关而与时滞无关.

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收稿日期: 2013-09-03

PACS:

O177.29

基金资助:国家自然科学基金（11201037，11371071和11871117）以及辽宁省自然科学基金201602190资助项目.

引用本文:

郑福, 聂坤, 郭宝珠. 具有内部控制和边界观测具有时滞的单管热交换方程的指数稳定性[J]. 应用数学学报, 2019, 42(2): 266-277. ZHENG Fu, ZHANG Yang, GUO Baozhu. Heat Exchanger Equation with Inner Control four and Boundary Observation with Delay. Acta Mathematicae Applicatae Sinica, 2019, 42(2): 266-277.

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