Inverse problems for a Boussinesq system for incompressible viscoelastic fluids
Antontsev S.N. Khompysh K.
June 2023John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2023#46Issue 911130 - 11156 pp.
In this paper, we study two inverse problems for the nonlinear Boussinesq system for incompressible viscoelastic nonisothermal 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 (Formula presented.) 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.
Boussinesq system , inverse problem , Kelvin–Voigt equations , unique solvability , viscoelastic incompressible fluids
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CMAFCIO - Universidade de Lisboa, Lisboa, Portugal
Lavrentyev Institute of Hydrodynamics, SB RAS, Novosibirsk, Russian Federation
Al-Farabi Kazakh National University, Almaty, Kazakhstan
CMAFCIO - Universidade de Lisboa
Lavrentyev Institute of Hydrodynamics
Al-Farabi Kazakh National University
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