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December  2018, 13(4): 585-607. doi: 10.3934/nhm.2018027

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

 1 Dipartimento di Scienze Aziendali-Management e Innovation Systems, University of Salerno, Via Giovanni Paolo Ⅱ, 132, Fisciano, SA, Italy 2 Department of System Analysis, National Mining University, Yavornitskii av., 19, 49005 Dnipro, Ukraine 3 Institute for Applied System Analysis of National Academy of Sciences and Ministry of Education and Science of Ukraine, Peremogy av., 37/35, IASA, 03056 Kyiv, Ukraine 4 Department of Information and Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo Ⅱ, 132, Fisciano, SA, Italy

* Corresponding author: Rosanna Manzo

Received  December 2017 Revised  August 2018 Published  November 2018

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 Robin-type 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.

Citation: Ciro D'Apice, Olha P. Kupenko, Rosanna Manzo. On boundary optimal control problem for an arterial system: First-order optimality conditions. Networks & Heterogeneous Media, 2018, 13 (4) : 585-607. doi: 10.3934/nhm.2018027
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