Optimum control of parabolic system with the distributed parameters on the graph

The initial and regional task for the parabolic equation with distributed is considered parameters on limited graph $\Gamma$ and it the corresponding problem of optimum control. Work continues researches of the author in the direction of existence and uniqueness optimum control in a case, when a condition of differential system an essence display of a piece of $[0,T]$ ($T<\infty$) in special space. Thus in quality of space of managements the space of functions integrated with a square is used $L_2(\Gamma_T)$, $\Gamma_T=\Gamma\times(0,T)$. Bibliogr. 13.