Geodesic
The existence problem of feedback control for one fractional Voigt model
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 4, pp. 621-642

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In this paper, we study the feedback control problem for a mathematical model that describes the motion of a viscoelastic fluid with memory along velocity field trajectories. We prove the existence of an optimal control that gives a minimum to a given bounded and semi-continuous from below quality functional. The proof uses the approximation-topological approach, the theory of regular Lagrangian flows, and the theory of topological degree for multivalued vector fields.
Mots-clés : fractional Voigt model
Keywords: viscoelastic fluid, motion with memory, optimal control, approximation-topological approach, regular Lagrangian flow, topological degree, multivalued vector field. 
@article{CMFD_2023_69_4_a4,
     author = {A. V. Zvyagin and E. I. Kostenko},
     title = {The existence problem of feedback control for one fractional {Voigt} model},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {621--642},
     publisher = {mathdoc},
     volume = {69},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_4_a4/}
}
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A. V. Zvyagin; E. I. Kostenko. The existence problem of feedback control for one fractional Voigt model. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 4, pp. 621-642. http://geodesic.mathdoc.fr/item/CMFD_2023_69_4_a4/