In this paper necessary and sufficient conditions of L∞-controllability and approximate L∞-controllability are obtained for the control system wtt = wxx - q2w, w(0,t) = u(t), x > 0, t ∈ (0,T), where q ≥ 0, T > 0, u ∈ L∞(0,T) is a control. This system is considered in the Sobolev spaces.
Mots clés : wave equation, half-axis, controllability problem, influence operator, Fourier transform, Sobolev space, Moore-Penrose inverse
@article{COCV_2012__18_3_748_0, author = {Fardigola, Larissa V.}, title = {Controllability problems for the {1-D} wave equation on a half-axis with the {Dirichlet} boundary control}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {748--773}, publisher = {EDP-Sciences}, volume = {18}, number = {3}, year = {2012}, doi = {10.1051/cocv/2011169}, mrnumber = {3041663}, zbl = {1252.93023}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2011169/} }
TY - JOUR AU - Fardigola, Larissa V. TI - Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 748 EP - 773 VL - 18 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011169/ DO - 10.1051/cocv/2011169 LA - en ID - COCV_2012__18_3_748_0 ER -
%0 Journal Article %A Fardigola, Larissa V. %T Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 748-773 %V 18 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011169/ %R 10.1051/cocv/2011169 %G en %F COCV_2012__18_3_748_0
Fardigola, Larissa V. Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 748-773. doi : 10.1051/cocv/2011169. http://www.numdam.org/articles/10.1051/cocv/2011169/
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