Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids

Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids Full article

Journal

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Output data

Year: 2024, Volume: 45, Number: 4, Pages: 1349-1365 Pages count : 17 DOI: 10.1134/s1995080224601152

Tags

inverse problem, heat convection, Kelvin–Voigt equations, non-Newtonian fluids, existence, uniqueness

Authors

Antontsev S.N. ¹ , Khompysh Kh. ²

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
2	Al-Farabi Kazakh National University, Almaty, Kazakhstan

The paper deals the study some inverse source problems for heat convection system which consists of Kelvin–Voigt equations governing an incompressible viscoelastic non-Newtonian flows and a heat equation. The studying inverse problems consist of recovering a time depended intensity f(t) of a density of external forces and an intensity j(t) of a heat source, in addition to a velocity v, a pressure π, and a temperature θ. As an additional information two types of integral overdetermination conditions over the domain are considered. For nonlinear inverse problem, under suitable conditions on the data, the local in time existence and uniqueness of weak and strong solutions are established. Some special cases of original inverse problem also investigated which allow global unique solvability.

Antontsev S.N. , Khompysh K.
Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids
Lobachevskii Journal of Mathematics. 2024. V.45. N4. P.1349-1365. DOI: 10.1134/s1995080224601152 РИНЦ

Submitted:	Jan 15, 2024
Accepted:	Mar 11, 2024
Published print:	Aug 22, 2024

Elibrary:

68640833

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