On the Optimal Control Problem for Vibrations of the Rod/String Consisting of Two Non-Homogeneous Sections with the Condition at an Intermediate Time

We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The describes the longitudinal vibrations non-homogeneous rod or transverse string given initial, intermediate, and final conditions. assume that travel time each sections is same. carried out by shifting one end other fixed. quality criterion set on entire interval. A constructive approach to building proposed. results obtained are illustrated analytical example.