Geodesic
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

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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.

DOI : 10.1051/cocv/2011169
Classification : 93B05, 35B37, 35L05
Keywords: wave equation, half-axis, controllability problem, influence operator, Fourier transform, Sobolev space, Moore-Penrose inverse 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv/2011169/}
}
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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

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