APPLICATION OF THE SHORTENING METHOD TO CONSTRUCTING AN ALMOST PERIODIC SOLUTION OF EVOLUTIONARY EQUATIONS - Ysmagul Р.; Utemissova А.; Tastanov М.; Mayer Ф.Ф.; Zhumartova Б. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2025)
The existence of almost periodic solutions for various classes of evolutionary systems is an important problem in the theory of oscillations. For example, the problem of the existence of almost periodic solutions with values ​​in metric space is considered within the framework of the theory of simple almost periodic differential equations. The study of almost periodic, as well as one-dimensional and multidimensional periodic oscillations is of particular importance. When considering many problems in mechanics, physics, and engineering, it is necessary to study such oscillatory solutions of evolutionary equations with simple and independent derivatives. In the present work, the use of the reduction method by independent variables and obtaining an efficient estimate of the deviations of almost multiperiod solutions of basic reduced systems is studied. The establishment of sufficient conditions for the existence and uniqueness of almost multiperiod solutions of first-order evolutionary equations is considered