О начально-краевой задаче, порождающей внутреннюю задачу сопряжения

In the paper, some initial-boundary value problem of mathematical physio is considered. The problem generates interim transmission problem that was investigated earlier. Time derivative into the equation, and the fixed complex parameter enters into the boundary condition. $\textit{The purpose of the work}$ is to show application of the operator method for studying of this initial-boundary value problem.