Volume 8, 2000Contrôle des systèmes gouvernés par des équations aux dérivées partielles
|Page(s)||95 - 105|
|Published online||15 August 2002|
On exact controllability of generic trees
Fakultät für Mathematik und Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
2 Departamento de Matematica Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
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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