Geodesic
On the Neumann boundary controllability for the non-homogeneous string on a half-axis
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012), pp. 307-335

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In the paper, the equation of a vibrating non-homogeneous string, whose potential is not equal to a constant, is considered on a half-axis. The Neumann control of the class $L^\infty$ is considered at a point $x=0$. The control problem is studied in the Sobolev spaces. The sufficient conditions for nullcontrollability and approximate null-controllability at a free time $T>0$ are obtained for the given system. The controls solving these problems are found explicitly. 
@article{JMAG_2012_8_a0,
     author = {K. S. Khalina},
     title = {On the {Neumann} boundary controllability for the non-homogeneous string on a half-axis},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {307--335},
     publisher = {mathdoc},
     volume = {8},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2012_8_a0/}
}
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K. S. Khalina. On the Neumann boundary controllability for the non-homogeneous string on a half-axis. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012), pp. 307-335. http://geodesic.mathdoc.fr/item/JMAG_2012_8_a0/