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Dager Salomon, Rene (2016). Approximate controllability of coupled 1-d wave equations onstar-shaped graphs. "Comptes Rendus Mathematique", v. 354 (n. 8); pp. 778-782. ISSN 1631-073X. https://doi.org/10.1016/j.crma.2016.05.006.
Title: | Approximate controllability of coupled 1-d wave equations onstar-shaped graphs |
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Author/s: |
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Item Type: | Article |
Título de Revista/Publicación: | Comptes Rendus Mathematique |
Date: | August 2016 |
ISSN: | 1631-073X |
Volume: | 354 |
Subjects: | |
Faculty: | E.T.S. de Ingeniería Agronómica, Alimentaria y de Biosistemas (UPM) |
Department: | Matemática Aplicada |
Creative Commons Licenses: | Recognition - No derivative works - Non commercial |
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In this Note, we study the approximate controllability of a cascade system of two 1-d wave equations defined on a star-shaped planar graph. Only the first equation is controlled, with controls applied at the simple vertices. The controls act on the second equation through the coupling at the multiple vertex. We give a necessary and sufficient condition for the approximate controllability of the system: all the ratios of the lengths of any two different edges of the graph should be irrational numbers. The result implies that, under these conditions, the approximate desensitizing controllability of a star-shaped network of strings holds, when the desensitized functional is the L2-norm of the displacement of the multiple node.
Type | Code | Acronym | Leader | Title |
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Government of Spain | MTM2013-42907-P | Unspecified | Universidad Politécnica de Madrid | Problemas inversos en lubricación industrial y otros problemas no lineales |
Item ID: | 48742 |
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DC Identifier: | https://oa.upm.es/48742/ |
OAI Identifier: | oai:oa.upm.es:48742 |
DOI: | 10.1016/j.crma.2016.05.006 |
Official URL: | http://www.sciencedirect.com/science/article/pii/S1631073X16300796?via%3Dihub |
Deposited by: | Memoria Investigacion |
Deposited on: | 18 Jan 2018 08:50 |
Last Modified: | 18 Jan 2018 08:50 |