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

On boundary optimal control problem for an arterial system: Existence of feasible solutions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

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

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References (35)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-018-0460-4
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Jun 22, 2018

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