变系数耦合抛物方程边界能控性的必要条件

兰州理工大学学报 ›› 2022, Vol. 48 ›› Issue (2): 156-162.

变系数耦合抛物方程边界能控性的必要条件

谢伟松^*, 张青青

天津大学数学学院, 天津 300350

收稿日期:2021-03-09 出版日期:2022-04-28 发布日期:2022-05-07
通讯作者: 谢伟松(1967-),男,湖南湘乡人,教授.Email:weis_xie@tju.edu.cn
基金资助:
天津市自然科学基金(18JCQNJC05400)

A necessary condition for boundary controllability of coupled parabolic equations with variable coefficients

XIE Wei-song, ZHANG Qing-qing

School of Mathematics, Tianjin University, Tianjin 300350, China

Received:2021-03-09 Online:2022-04-28 Published:2022-05-07

摘要/Abstract

摘要： 研究了非标量变系数线性抛物型方程的边界能控性. 通过在边界处施加一个控制,建立具有相同时间依赖性系数的两方程系统的边界能控性的一个必要条件.并基于方程的可观测不等式,证明了该必要条件.

关键词: 耦合抛物方程, 零能控性, 观测不等式

Abstract: The boundary controllability of non-scalar variable coefficient linear parabolic equations is studied. A necessary condition for boundary null controllability is established, which has only one boundary control for a system with two equations depending on the same coefficient that is time-dependent. The necessary condition is proved based on the observability inequality of the equations.

Key words: coupled parabolic equations, null controllability, observability inequality

中图分类号:

O231.1

谢伟松, 张青青. 变系数耦合抛物方程边界能控性的必要条件[J]. 兰州理工大学学报, 2022, 48(2): 156-162.

XIE Wei-song, ZHANG Qing-qing. A necessary condition for boundary controllability of coupled parabolic equations with variable coefficients[J]. Journal of Lanzhou University of Technology, 2022, 48(2): 156-162.

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