We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace of . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in and satisfy certain restriction on their total impact on with respect to the time-variable.
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}, mrnumber = {2209352}, zbl = {1105.93011}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2006001/} }
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 PY - 2006 SP - 231 EP - 252 VL - 12 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2006001/ DO - 10.1051/cocv:2006001 LA - en ID - COCV_2006__12_2_231_0 ER -
%0 Journal Article %A Khapalov, Alexander Y. %T Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 231-252 %V 12 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2006001/ %R 10.1051/cocv:2006001 %G en %F COCV_2006__12_2_231_0
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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