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

Ciro D'Apice; Olha P. Kupenko; Rosanna Manzo; Ciro D'Apice; Olha P. Kupenko; Rosanna Manzo

doi:10.3934/nhm.2018027

Networks and Heterogeneous Media

2018, Volume 13, Issue 4: 585-607. doi: 10.3934/nhm.2018027

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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

Received: 01 December 2017 Revised: 01 August 2018
Primary: 35K51, 35B45; Secondary: 49J20

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.
- Boussinesq-type system,
- existence result,
- first-order optimality conditions,
- optimal solutions
Citation: Ciro D'Apice, Olha P. Kupenko, Rosanna Manzo. On boundary optimal control problem for an arterial system: First-order optimality conditions[J]. Networks and Heterogeneous Media, 2018, 13(4): 585-607. doi: 10.3934/nhm.2018027

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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 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.

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