| Issue |
ESAIM: COCV
Volume 18, Number 3, July-September 2012
|
|
|---|---|---|
| Page(s) | 748 - 773 | |
| DOI | https://doi.org/10.1051/cocv/2011169 | |
| Published online | 19 September 2011 | |
Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control
Mathematical Division, Institute for Low Temperature Physics and
Engineering, 47 Lenin
Ave., 61103
Kharkiv,
Ukraine
fardigola@ukr.net
Received:
2
September
2010
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.
Mathematics Subject Classification: 93B05 / 35B37 / 35L05
Key words: Wave equation / half-axis / controllability problem / influence operator / Fourier transform / Sobolev space / Moore-Penrose inverse
© EDP Sciences, SMAI, 2011
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