Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory
This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/1026 |
| _version_ | 1797530988159434752 |
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| author | Mikhail A. Artemov |
| author_facet | Mikhail A. Artemov |
| author_sort | Mikhail A. Artemov |
| collection | DOAJ |
| description | This paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included in the initial condition. The objective of control is to match the velocity field at the final time with a prescribed target field. The control model under consideration is interpreted as a continuous evolution system in an infinite-dimensional Hilbert space. The existence of at least one optimal control is proved under inclusion-type constraints for admissible controls. |
| first_indexed | 2024-03-10T10:37:42Z |
| format | Article |
| id | doaj.art-07b2d67b65ce486a84e40ba9b9d4392a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:37:42Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-07b2d67b65ce486a84e40ba9b9d4392a2023-11-21T23:09:12ZengMDPI AGSymmetry2073-89942021-06-01136102610.3390/sym13061026Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with MemoryMikhail A. Artemov0Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, RussiaThis paper deals with an optimization problem for a nonlinear integro-differential system that describes the unsteady plane motion of an incompressible viscoelastic fluid of Jeffreys–Oldroyd type within a fixed bounded region subject to the no-slip boundary condition. Control parameters are included in the initial condition. The objective of control is to match the velocity field at the final time with a prescribed target field. The control model under consideration is interpreted as a continuous evolution system in an infinite-dimensional Hilbert space. The existence of at least one optimal control is proved under inclusion-type constraints for admissible controls.https://www.mdpi.com/2073-8994/13/6/1026optimization problemintegro-differential systemcontrol operatorexistence theoremnon-Newtonian fluidJeffreys–Oldroyd viscoelastic fluid |
| spellingShingle | Mikhail A. Artemov Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory Symmetry optimization problem integro-differential system control operator existence theorem non-Newtonian fluid Jeffreys–Oldroyd viscoelastic fluid |
| title | Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory |
| title_full | Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory |
| title_fullStr | Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory |
| title_full_unstemmed | Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory |
| title_short | Solvability of an Optimization Problem for the Unsteady Plane Flow of a Non-Newtonian Fluid with Memory |
| title_sort | solvability of an optimization problem for the unsteady plane flow of a non newtonian fluid with memory |
| topic | optimization problem integro-differential system control operator existence theorem non-Newtonian fluid Jeffreys–Oldroyd viscoelastic fluid |
| url | https://www.mdpi.com/2073-8994/13/6/1026 |
| work_keys_str_mv | AT mikhailaartemov solvabilityofanoptimizationproblemfortheunsteadyplaneflowofanonnewtonianfluidwithmemory |