Generalized solutions of a boundary value problem for thermal conductivity equation on a graph

Generalized solutions of a boundary value problem for thermal conductivity equation on an arbitrary graph are considered. Analogues of corresponding Sobolev spaces which are dense sets in the space of square-integrable functions are constructed. The theorem of unique solvability of a boundary-value problem is proved. The algorithm of determining boundary control in the problem of translating a differential system from the initial state to the desired final one is presented. Bibliogr. 4.