梯形区域上一维波动方程的内点观测  

Internal Point Observation of One-dimensional Wave Equations in a Trapezoid Domain

作　　者：逯丽清[1] 石雨点 LU Liqing;SHI Yudian(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2021年第3期471-477,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11871315)。

摘　　要：研究了在梯形区域内具有混合边界的一维波动方程,借助于广义傅立叶级数和加权L2-空间中的Parseval等式,分别导出了内部固定点和内部移动点的能观性不等式,并获得了对应耦合系统的同时精确能控性。By mean of generalized Fourier series and Parseval’s equality in weighted L2-spaces, a one-dimensional wave equation with mixed boundary in trapezoid domains is studied. The observability inequalities at the internal fixed point and the internal moving point are derived respectively, and the simultaneous exact controllability of the corresponding coupled system is obtained.

关 键 词：梯形区域 混合边界 内点观测 精确能控性 

分 类 号：O231[理学—运筹学与控制论]