| Title:
|
Remark on stabilization of tree-shaped networks of strings (English) |
| Author:
|
Ammari, Kaïs |
| Author:
|
Jellouli, Mohamed |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
327-343 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
networks of strings |
| Keyword:
|
input-output map |
| Keyword:
|
well-posed system |
| MSC:
|
35B37 |
| MSC:
|
93B07 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 1164.93315 |
| idMR:
|
MR2324731 |
| DOI:
|
10.1007/s10492-007-0018-1 |
| . |
| Date available:
|
2009-09-22T18:30:11Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134679 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
