Free vibrations of axially moving strings: Energy estimates and boundary observability

被引：0
|
作者：
Ghenimi, Seyf Eddine [1 ]
Sengouga, Abdelmouhcene [1 ,2 ]
机构：
[1] Univ MSila, Lab Funct Anal & Geometry Spaces, Msila, Algeria
[2] Univ MSila, Dept Math, PB 166, Msila 28000, Algeria
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 13期
关键词：
axially moving strings; boundary observability; energy estimates; Fourier series; WAVE-EQUATION; CONTROLLABILITY;
D O I：
10.1002/mma.9285
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients are explicitly computed in function of the initial data. We also define an energy expression for the solution that is conserved in time. Then, we establish boundary observability inequalities with explicit constants.
引用
收藏
页码：13716 / 13730
页数：15
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