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INVERSE PROBLEMS FOR A BOUSSINESQ SYSTEM FOR INCOMPRESSIBLE VISCOELASTIC FLUIDS
  • Khonatbek Khompysh,
  • Stanilslav Antontsev
Khonatbek Khompysh
Al-Farabi Kazakh National University

Corresponding Author:konat_k@mail.ru

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Stanilslav Antontsev
Universidade de Lisboa Faculdade de Ciencias
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Abstract

In this paper, we study two inverse problems for the nonlinear Boussinesq system for incompressible viscoelastic non-isothermal Kelvin-Voigt fluids. The studying inverse problems consist of determining an intensities of density of external forces and heat source under given integral overdetermination conditions. Two types of boundary conditions for the velocity v are considered: sticking and sliding conditions on boundary. In both cases of these boundary conditions, the local and global in time existence and uniqueness of weak and strong solutions are established under suitable assumptions on the data. The large time behavior of weak solutions is also studied.
10 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
15 Sep 2022Submission Checks Completed
15 Sep 2022Assigned to Editor
21 Sep 2022Reviewer(s) Assigned
08 Jan 2023Review(s) Completed, Editorial Evaluation Pending
09 Jan 2023Editorial Decision: Revise Minor
11 Jan 20231st Revision Received
14 Jan 2023Submission Checks Completed
14 Jan 2023Assigned to Editor
14 Jan 2023Review(s) Completed, Editorial Evaluation Pending
18 Jan 2023Reviewer(s) Assigned
14 Feb 2023Editorial Decision: Accept