Partial averaging of the systems on time scales
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 1
Abstract
The scheme of partial averaging of systems with small parameter on time scales was established. A proximity of solutions of given and partially averaged system of equations was proved under sufficiently general conditions. Obtained results extend an application area for previously developed numerically–asymptotic method of solution for optimal control problems on time scales.
Authors and Affiliations
A. P. Ogulenko
Keywords
Related Articles
- EP ID EP342729
- DOI -
- Views 77
- Downloads 0
Asymptotical expansion of vanishing solutions of differential equations in one special case
Considered in this paper is a system of quasilinear differential equations with factors on the right side that disappear when 𝑡 → ∞ ( absolutely integrable or not). Sufficient conditions are obtained under which it is po...
Influence of plastic zone near the tip of interfacial crack on the contact of its lips
We have developed a complex model of the prefracture zone near the tip of an interface crack that assumes the existence, in its vicinity, of a small-scale contact region of its faces interacting according to the law of d...
ON A REDUCTION OF A LINEAR HOMOGENEOUS DIFFERENTIAL SYSTEM WITH OSCILLATING COEFFICIENTS TO A SYSTEM WITH SLOWLY VARYING COEFFICIENTS IN RESONANCE CASE
For the linear homogeneous differential system, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, conditions of existence of the l...
ABOUT CONVERGENCE OF THE GENERALIZED HARMONIC SERIES WHEN THE SIGNS OF ITS SUMMANDS ARE CHANGED
In this paper we study the question about convergence of the generalized harmonic series when the signs of its summands are changed. For this we consider the sequence of numbers where the sign is switched. The main resul...
To the theory of Hilbert space’s unconditional basis from values of entire vector-functions
Classes of entire functions of exponential type are considered in the article. They fulfil certain conditions related to theorems about unconditional basises from the values of entire vectorfunctions. In particular, for...