On the Neumann Boundary Controllability for the Non-Homogeneous String on a Half-Axis

摘要

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 ^∞ is considered at a point x = 0. The control problem is studied in the Sobolev spaces. The suffcient 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.