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 a control object is described by an initial-boundary value problem for 1D system of pseudo-parabolic nonlinear equations with an unbounded coefficient in the principal part and Robin boundary conditions. The main question we discuss in this part of paper is about topological and algebraical properties of the set of feasible solutions. Following Faedo–Galerkin method, we establish the existence of weak solutions to the corresponding initial-boundary value problem and show that these solutions possess some special extra regularity properties which play a crucial role in the proof of solvability of the original optimal control problem.
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