IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p275-d489884.html
   My bibliography  Save this article

Optimal Control for a Nonlocal Model of Non-Newtonian Fluid Flows

Author

Listed:
  • Evgenii S. Baranovskii

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

  • Mikhail A. Artemov

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

Abstract

This paper deals with an optimal control problem for a nonlocal model of the steady-state flow of a differential type fluid of complexity 2 with variable viscosity. We assume that the fluid occupies a bounded three-dimensional (or two-dimensional) domain with the impermeable boundary. The control parameter is the external force. We discuss both strong and weak solutions. Using one result on the solvability of nonlinear operator equations with weak-to-weak and weak-to-strong continuous mappings in Sobolev spaces, we construct a weak solution that minimizes a given cost functional subject to natural conditions on the model data. Moreover, a necessary condition for the existence of strong solutions is derived. Simultaneously, we introduce the concept of the marginal function and study its properties. In particular, it is shown that the marginal function of this control system is lower semicontinuous with respect to the directed Hausdorff distance.

Suggested Citation

  • Evgenii S. Baranovskii & Mikhail A. Artemov, 2021. "Optimal Control for a Nonlocal Model of Non-Newtonian Fluid Flows," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:275-:d:489884
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/275/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/275/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chemetov, Nikolai & Cipriano, Fernanda, 2018. "Optimal control for two-dimensional stochastic second grade fluids," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2710-2749.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:275-:d:489884. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.