# Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 2, page 231-252
- ISSN: 1292-8119

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topKhapalov, Alexander Y.. "Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping." ESAIM: Control, Optimisation and Calculus of Variations 12.2 (2006): 231-252. <http://eudml.org/doc/249674>.

@article{Khapalov2006,

abstract = {
We show that the set of nonnegative equilibrium-like states, namely, like $ (y_d, 0) $ of the semilinear vibrating string that can be reached from any non-zero initial state $ (y_0, y_1) \in H^1_0 (0,1) \times L^2 (0,1)$, by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace $ L^2 (0,1) \times \\{0\\} $ of $ L^2 (0,1) \times H^\{-1\} (0,1)$. Our main results deal with nonlinear terms which admit at most the linear
growth at infinity in $ \; y \; $ and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.
},

author = {Khapalov, Alexander Y.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Semilinear wave equation; approximate controllability; multiplicative controls; axial load; damping. ; semilinear wave equation; damping},

language = {eng},

month = {3},

number = {2},

pages = {231-252},

publisher = {EDP Sciences},

title = {Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping},

url = {http://eudml.org/doc/249674},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Khapalov, Alexander Y.

TI - Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/3//

PB - EDP Sciences

VL - 12

IS - 2

SP - 231

EP - 252

AB -
We show that the set of nonnegative equilibrium-like states, namely, like $ (y_d, 0) $ of the semilinear vibrating string that can be reached from any non-zero initial state $ (y_0, y_1) \in H^1_0 (0,1) \times L^2 (0,1)$, by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace $ L^2 (0,1) \times \{0\} $ of $ L^2 (0,1) \times H^{-1} (0,1)$. Our main results deal with nonlinear terms which admit at most the linear
growth at infinity in $ \; y \; $ and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.

LA - eng

KW - Semilinear wave equation; approximate controllability; multiplicative controls; axial load; damping. ; semilinear wave equation; damping

UR - http://eudml.org/doc/249674

ER -

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