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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Controllability Properties of a Vibrating String with Variable Axial Load Only
verfasst von : Alexander Y. Khapalov
Erschienen in: Controllability of Partial Differential Equations Governed by Multiplicative Controls
Verlag: Springer Berlin Heidelberg
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We show that the set of equilibrium-like states (y
d
,0) of a vibrating string which can approximately be reached in the energy space H
1
0
(0,1)× L
2
(0,1) from almost any non-zero initial datum, namely, (y
0
,y
1
) ε (H
2
(0,1)∩H
1
0
(0,1))× H
1
(0,1), (y
0
,y
1
) ≠ (0,0) by varying its axial load only is dense in the subspace H
1
0
(0,1)× {0} of this space. This result is based on a constructive argument and makes use of piecewise constant-in-time control functions (loads) only, which enter the model equation as coefficients.