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Issue ESAIM: Proc.
Volume 8, 2000
Contrôle des systèmes gouvernés par des équations aux dérivées partielles
Page(s) 95 - 105
DOI http://dx.doi.org/10.1051/proc:2000007

ESAIM: Proc., 2000, Vol. 8, pp. 95-105
DOI: 10.1051/proc:2000007

On exact controllability of generic trees

Günter Leugering1 and 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


Abstract
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.



© EDP Sciences, ESAIM 2000


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