Geodesic
Local boundary controllability in classes of differentiable functions for the wave equation
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 52-64

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The well-known fact following from the Holmgren–John–Tataru uniqueness theorem is a local approximate boundary $L_2$-controllability of the dynamical system governed by the wave equation. Generalizing this result, we establish the controllability in certain classes of differentiable functions in the domains filled up with waves. 
@article{ZNSL_2017_461_a2,
     author = {M. I. Belishev},
     title = {Local boundary controllability in classes of differentiable functions for the wave equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--64},
     publisher = {mathdoc},
     volume = {461},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a2/}
}
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M. I. Belishev. Local boundary controllability in classes of differentiable functions for the wave equation. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 52-64. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a2/