Approximate controllability of coupled 1-d wave equations onstar-shaped graphs

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.

Description

Title: Approximate controllability of coupled 1-d wave equations onstar-shaped graphs
Author/s:
  • Dager Salomon, Rene
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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Abstract

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.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2013-42907-PUnspecifiedUniversidad Politécnica de MadridProblemas inversos en lubricación industrial y otros problemas no lineales

More information

Item ID: 48742
DC Identifier: http://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
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