Journal of Evolution Equations

, Volume 18, Issue 4, pp 1745–1786 | Cite as

On boundary optimal control problem for an arterial system: Existence of feasible solutions

  • Ciro D’Apice
  • Maria Pia D’Arienzo
  • Peter I. Kogut
  • Rosanna ManzoEmail author


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.


Boussinesq-type system Existence result Faedo–Galerkin method Feasible solutions 

Mathematics Subject Classification

35K51 35B45 49J20 58F15 58F17 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ciro D’Apice
    • 1
  • Maria Pia D’Arienzo
    • 2
  • Peter I. Kogut
    • 3
  • Rosanna Manzo
    • 2
    Email author
  1. 1.Dipartimento di Scienze Aziendali-Management e Innovation SystemsUniversity of SalernoFiscianoItaly
  2. 2.Department of Information and Electrical Engineering and Applied MathematicsUniversity of SalernoFiscianoItaly
  3. 3.Department of Differential EquationsOles Honchar Dnipro National UniversityDniproUkraine

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