Inverse Source Problems for Kelvin–Voigt System With Final Overdetermination Condition
Cheng J. Khompysh K. Nugymanova N.
15 March 2026John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2026#49Issue 43317 - 3333 pp.
This paper is devoted to studying inverse source problems for the linear Kelvin–Voigt equations with memory, which govern the flow of incompressible viscoelastic fluids. The memory term is represented by an integral with convolution and reflects the elastic properties of the fluid. The inverse problems consist of recovering the spatial distribution of external forces (Formula presented.) by measurements for the velocity (Formula presented.) and gradient of pressure (Formula presented.) at the final moment (Formula presented.). These inverse problems are investigated in the following cases: with and without the memory term in the momentum equation, and under both sticking and sliding boundary conditions. In all cases, under suitable conditions on the data of the problem, the existence, uniqueness as well as the stability of strong solutions were established.
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Fudan University, Shanghai, China
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Fudan University
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026