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
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