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

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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. 
@article{MZM_2022_112_1_a2,
     author = {E. S. Baranovskii},
     title = {Feedback {Optimal} {Control} {Problem} for a {Network} {Model} of {Viscous} {Fluid} {Flows}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {31--47},
     publisher = {mathdoc},
     volume = {112},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a2/}
}
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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/