Mathematical models of evolutionary processes on the network and setepodobnoj area. The method, which applies to many tasks of optimal control of differential systems, the status of which is defined by the weak solutions of evolutionary equations of mathematical physics on networks and setepodobnyh areas. This method is very common and is applicable to a wide class of linear tasks that have an interesting analogy with also multi-phase tasks of mechanics (in particular, the theory of plasticity). The results obtained in this manner for a specific equation with distributed parameters in the setepodobnoj area, serve not only to demonstrate the method, but also of interest to applications.