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, Tome 12 (2006) no. 2, pp. 231-252.

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 )H 0 1 (0,1)×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)×{0} of L 2 (0,1)×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.

DOI : https://doi.org/10.1051/cocv:2006001
Classification : 93,  35
Mots clés : semilinear wave equation, approximate controllability, multiplicative controls, axial load, damping
@article{COCV_2006__12_2_231_0,
     author = {Khapalov, Alexander Y.},
     title = {Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {231--252},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {2},
     year = {2006},
     doi = {10.1051/cocv:2006001},
     zbl = {1105.93011},
     mrnumber = {2209352},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2006001/}
}
Khapalov, 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, Tome 12 (2006) no. 2, pp. 231-252. doi : 10.1051/cocv:2006001. http://www.numdam.org/articles/10.1051/cocv:2006001/

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