On boundary optimal control problem for an arterial system: First-order optimality conditions

Abstract

We discuss a control constrained boundary optimal control problem for the Boussinesq-type system arising in the study of the dynamics of an arterial network. We suppose that the control object is described by an initial-boundary value problem for 1D system of pseudo-parabolic nonlinear equations with an unbounded coefficient in the principle part and the Robintype of boundary conditions. The main question we study in this part of the paper is about the existence of optimal solutions and first-order optimality conditions.