Abstract
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.