Geodesic
On exact controllability of generic trees
Günter Leugering1 ; Enrique Zuazua2
1 Fakultät für Mathematik und Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
2 Departamento de Matematica Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
ESAIM. Proceedings, Tome 8 (2000), pp. 95-105 Cet article a éte moissonné depuis la source EDP Sciences

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We consider a divining rod as an exemplaric network of elastic homogeneous strings. If the lengths of the strings are rationally dependent, it is known that even approximate controllability by a single boundary control fails, whenever the other two simple nodes satisfy the same boundary condition. In this paper we give a positive answer to the question whether exact controllability for some class of initial/final data holds, if the individual lengths of the strings are no longer rationally dependent. In order to do this, we resort to a special class of algebraic numbers, namely Roth's class. However, we do not use Fourier series expansions but rather d'Alembert's formula to analyze the propagation of the effect of the controllers along the network.
DOI : 10.1051/proc:2000007

Günter Leugering 1 ; Enrique Zuazua 2

1 Fakultät für Mathematik und Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
2 Departamento de Matematica Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain 
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     author = {G\"unter Leugering and Enrique Zuazua},
     title = {On exact controllability of generic trees},
     journal = {ESAIM. Proceedings},
     pages = {95--105},
     year = {2000},
     volume = {8},
     doi = {10.1051/proc:2000007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2000007/}
}
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Günter Leugering; Enrique Zuazua. On exact controllability of generic trees. ESAIM. Proceedings, Tome 8 (2000), pp. 95-105. doi: 10.1051/proc:2000007

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