Remark on stabilization of tree-shaped networks of strings

被引：0
作者：
Kaïs Ammari
Mohamed Jellouli
机构：
[1] Faculty of Sciences of Monastir,Department of Mathematics
来源：
Applications of Mathematics | 2007年 / 52卷
关键词：
networks of strings; input-output map; well-posed system;
D O I：
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学科分类号：
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.
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页码：327 / 343
页数：16
相关论文
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