Remark on stabilization of tree-shaped networks of strings

被引：37

作者：

Ammari, Kais ^{[1
]}

Jellouli, Mohamed ^{[1
]}

机构：

[1] Fac Sci Monastir, Dept Math, Monastir 5019, Tunisia

来源：

APPLICATIONS OF MATHEMATICS | 2007年 / 52卷 / 04期

关键词：

networks of strings; input-output map; well-posed system;

D O I：

10.1007/s10492-007-0018-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a tree-shaped network of vibrating elastic strings, with feedback acting on the root of the tree. Using the d'Alembert representation formula, we show that the input-output map is bounded, i.e. this system is a well-posed system in the sense of G. Weiss (Trans. Am. Math. Soc. 342 (1994), 827-854). As a consequence we prove that the strings networks are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data.

引用

页码：327 / 343

页数：17

共 14 条

[1] Stabilization of second order evolution equations by a class of unbounded feedbacks [J].