Observability and Controllability of the 1-D Wave Equation in Domains with Moving Boundary

被引：11

作者：

Sengouga, Abdelmouhcene ^{[1
]}

机构：

[1] Univ Msila, Lab Funct Anal & Geometry Spaces, Msila 28000, Algeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2018年 / 157卷 / 01期

关键词：

Wave equation; Non-cylindrical domains; Observability; Controllability; Hilbert uniqueness method; Generalized Fourier series;

D O I：

10.1007/s10440-018-0166-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By mean of generalized Fourier series and Parseval's equality in weighted L-2-spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp time, at each of the endpoints of the interval. The observability constants are explicitly given. Using the Hilbert Uniqueness Method we deduce the exact boundary controllability of the wave equation.

引用

页码：117 / 128

页数：12

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