An inverse problem for Kelvin–Voigt equations perturbed by isotropic diffusion and damping

Khompysh K. Kenzhebai K.
15 May 2022 John Wiley and Sons Ltd

Mathematical Methods in the Applied Sciences
2022 #45 Issue 7 3817 - 3842 pp.

In this paper, we consider an inverse problem of finding a coefficient of right hand side of the following system of Kelvin–Voigt equations perturbed by an isotropic diffusion and damping terms (Formula presented.) (Formula presented.) The damping term γ|v|^{m − 2}v in the momentum equation realizes an absorbtion (sink) if γ ≤ 0, and a source if γ > 0. We show how the exponents p, m, the coefficients ν, ϰ, γ, the dimension of the space d, and data of the problem should interact each other for the existence of weak solutions to the problem. We also establish the conditions for uniqueness of the solutions to this problem.

existence , inverse problem , Kelvin–Voigt equation , p-Laplacian , uniqueness

Text of the article Перейти на текст статьи

Al-Farabi Kazakh National University, Almaty, Kazakhstan

Al-Farabi Kazakh National University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026