Optimal feedback control in the problem of the motion of a viscoelastic fluid

Abstract

We study an optimization problem for the feedback control system emerging as a regularized model for the motion of a viscoelastic fluid subject to the Jeffris-Oldroyd rheological relation. The approach includes systems governed by the classical Navier-Stokes equation as a particular case. Using the topological degree theory for condensing multimaps we prove the solvability of the approximating problem and demonstrate the convergence of approximate solutions to a solution of a regularized one. At last we show the existence of a solution minimizing a given convex, lower semicontinuous functional.

On a Multivalued Differential Equation with Nonlocality in Time

“…The optimal feedback control of a motion of a viscoelastic fluid via a multivalued differential equation is, e.g., considered in Gori et al [21] and Obukhovskiȋ, Zecca, and Zvyagin [31]. Existence of solutions for the equation are shown via topological degree theory.…”

On a multivalued differential equation with nonlocality in time

“…The optimal feedback control of a motion of a viscoelastic fluid via a multivalued differential equation is, e.g., considered in Gori et al [21] and Obukhovskiȋ, Zecca, and Zvyagin [26]. Existence of solutions for the equation are shown via topological degree theory.…”

Optimal feedback control problem for Bingham media motion with periodic boundary conditions

“…Такой подход позволил исследовать задачи управления ряда моделей движения неньютоновых сред (суспензий, водных растворов полимеров, различных сред с памятью [6][7][8][9][10][11][12]), которые в силу сложности этих систем ранее были недостаточно изучены с точки зрения оптимального управления.…”