Kelvin-Voigt equations with memory: existence, uniqueness and regularity of solutions

Жады мүшесi бар Кельвин-Фойгт теңдеулерi: шешiмдердiң бар болуы, жалғыздығы және регулярлығы
Уравнения Кельвина–Фойгта с памятью: существование, единственность и регулярность решений
Khompysh Kh. Nugymanova N.K.
2023 E.A. Buketov Karaganda University Publish house

Bulletin of the Karaganda University. Mathematics Series
2023 #112 Issue 4 66 - 78 pp.

In general, the study of inverse problems is realizable only in the case when the corresponding direct problems have the unique solution with some necessary properties such as continuity and regularity. In this paper, we study initial-boundary value problems for the system of 2D-3D nonlinear Kelvin-Voigt equations with memory, which describes a motion of an incompressible homogeneous non-Newtonian fluids with viscoelastic and relaxation properties. The investigation of these direct problems is related to the study of inverse problems for this system, which requires the continuity and regularity of solutions to these direct problems and their derivatives. The system, in addition to the initial condition, is supplemented with one of the boundary conditions: stick and slip boundary conditions. In both cases of these boundary conditions, the global in time existence and uniqueness of strong solutions to these initial-boundary value problems were proved. Moreover, under suitable assumptions on the data, the regularity of solutions and their derivatives were established.

global existence and uniqueness , Kelvin-Voigt system , slip and stick boundary conditions , smoothness , strong solutions

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