The Hoff equations on a graph with the multipoint initial-final value condition

We consider the Hoff equations on a graph. For these equations, we prove the unique solvability of the multipoint initial-final value problem, and construct an analytical solution. As an example, we consider the Hoff equations on a double-edge graph with a three-point initial-final value condition. The article, in addition to the introduction and bibliography, contains two parts. The first part presents theoretical information about Sobolev type equations, as well as construction of a solution to an abstract Sobolev type equation with the multipoint initial-final value condition. In the second part, we apply the obtained abstract results to a specific Hoff model.