On the Non-Linear Problem of Fluid Distribution Networks in Quasi-Steady Condition of Flow

The direct nonlinear problem of a fluid distribution network in unsteady state of flow is dealt within this paper Referring to a class of nonlinear flow equations several issues related to the mathematical well-posedness are analyzed. A mixed variational formulation in terms of the state variables of the network along with a weak formulation with respect to the time variable is associated to the classical differential algebraic problem formulation. The strict convexity of network functional and the uniform monotonicity of the operator resulting from the temporal discretization allow the proof of the uniqueness of the solution and provide a necessary condition for global stability.