Multiperiodic Bounded Oscillations in Quasilinear Finite-Hereditary Integro-Differential Systems Convection-Diffusion Type
Aitenova G.M. Sartabanov Z.A. Abdikalikova G.A.
August 2022Pleiades Publishing
Lobachevskii Journal of Mathematics
2022#43Issue 82046 - 2056 pp.
Abstract: The question of the existence of multiperiodic oscillations in linear and quasilinear systems describing finitely hereditary processes of the convective-diffusion type is investigated. Hereditary processes with a finite duration are characterized by an integral term with finite difference time limits. Diffusion—the presence in the system of the second derivative along the path—is the penetration of a substance into a continuous medium (water). The first derivative along the path from the desired one characterizes the movement of matter with a moving flow of a continuous medium. The almost periodicity in time of the process is described by the differentiation operator with respect to multidimensional time and the periodicity with respect to them. Thus, the flow due to multiperiodicity, convection, diffusion, and heredity has been considered. Sufficient conditions of multiperiodic oscillations in time variables in linear systems are established: a) with exponentially decreasing amplitude when moving along the semi-axis, b) with periodically varying amplitude when moving along a closed line. The result obtained in the case b) is extended to quasilinear systems.
composition of oscillation operators , convective , diffusion , finite-hereditary , integro-differential , matricant , matrix differentiation operator , multiperiodic
Text of the article Перейти на текст статьи
Utemisov West Kazakhstan University, Uralsk, Kazakhstan
Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
Utemisov West Kazakhstan University
Zhubanov Aktobe Regional University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026