Geodesic
Feedback Optimal Control Problem for a Network Model of Viscous Fluid Flows
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 31-47.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a feedback optimal control problem for a three-dimensional model of a stationary flow of a non-Newtonian fluid (with variable viscosity) in a pipeline network with complex geometry. The control parameter is the dynamic pressure on connection surfaces of pipes to nodes. The flow model is a mixed boundary-value problem for a system of strongly nonlinear partial differential equations in a netlike domain with Kirchhoff-type transmission conditions at interior nodes of the network. The solvability of the optimization problem in the weak formulation is proved; namely, we establish sufficient conditions for the existence of a weak solution which minimizes a lower semicontinuous cost functional.
Keywords: network model, non-Newtonian fluid, feedback control, Bernoulli boundary conditions, Kirchhoff transmission conditions, set-valued map, operator inclusion
Mots-clés : optimal solutions. 
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E. S. Baranovskii. Feedback Optimal Control Problem for a Network Model of Viscous Fluid Flows. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 31-47. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a2/

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