Vol 24, No 2 (2018)
- Year: 2018
- Articles: 7
- URL: https://journals.ssau.ru/est/issue/view/299
Full Issue
Articles
BOUNDARY VALUE PROBLEMS FOR COMPOSITE TYPE EQUATIONS WITH A QUASIPARABOLIC OPERATOR IN THE LEADING PART HAVING THE VARIABLE DIRECTION OF EVOLUTION AND DISCONTINUOUS COEFFICIENTS
Abstract
It is studied the solvability of boundary value problems for non-classical differential equations of Sobolev type with an alternating function, which has a discontinuity of the first kind at the point zero. Also, this function changes sign depending on the sign of the variable x. It is proved the existence and uniqueness theorems for regular solutions, which has all generalizated derivatives including in this equation. Presence of necessary a priori estimates for the solutions of the problems under study.
7-17
ON A PROBLEM WITH NON-LOCAL CONDITIONS FOR THE EQUATIONS OF THE IV ORDER
Abstract
The article deals with a non-local problem with an integral condition for pseudohyperbolic fourth order equation. The dominant mixed derivative which is presented in the equation allowed to interpret the task as an analogue of the Gurs problem. The conditions for the coefficients of the equation and
the input data were obtained to ensure the existence of a single task’s decision.
18-23
ФОРМА СВОЙСТВО ПРОСТРАНСТВА ВЕРОЯТНОСТНЫХ МЕР И ЕГО ПОДПРОСТРАНСТВ
Abstract
В этой заметке мы рассмотрим ковариантные функторы, действующие в категории компактов, сохраняющие формы бесконечных компактов, ANR -систем, движущиеся компакты, эквивалентность формы, гомотопическую эквивалентность и A(N)SR свойства компактов. Рассмотрены свойства формы компактного пространства X, состоящего из компонент связности 0 этого компактного X под действием ковариантных функторов. И мы изучаем равенство форм ShX = ShY бесконечных компактов для пространства вероятностных мер P(X) и его подпространств.
24-27
НЕКОТОРЫЕ ЗНАЧЕНИЯ ПОДФУНКТОРЫ МЕР ФУНКТОРОВ В КАТЕГОРИЯХ COMP
Abstract
Данная заметка посвящена сохранению подфункторами функтора P вероятностных мер пространств счетной размерности и экстензорным свойствам подпространств пространства вероятностных мер.
28-32
ON A PENDULUM MOTION IN MULTI-DIMENSIONAL SPACE. PART 3. DEPENDENCE OF FORCE FIELDS ON THE TENSOR OF ANGULAR VELOCITY
Abstract
In the proposed cycle of work, we study the equations of motion of dynamically symmetric fixed n-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of motion of a free n-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In this work, we study that case when the force fields linearly depend on the tensor of angular velocity.
33-54
ASYMPTOTIC REPRESENTATION OF THE STRESS FIELD NEAR THE CRACK TIP OF AN INFINITE PLATE WITH TWO SEMI-INFINITE SYMMETRICAL EDGE NOTCHES: THEORETICAL STUDY AND COMPUTATIONAL EXPERIMENT
Abstract
This article is aimed at theoretical study of the stress-strain state of an infinite plate with two semi-infinite symmetrical edge notches. The analytical solution is obtained by means of decomposition in the M. Williams series expansion and subsequent calculation of the amplitude coefficients of the expansion using the complex representation of stresses. An analysis of the multiparametric expansion of the stress field and a computational experiment with different number of terms are carried out. A comparison of the complex representation of the stress field with the asymptotic series of M. Williams
obtained shows the need for an accurate estimate of the number of terms keeping in the expansion series depending on the distance from the crack tip.
55-66
MODEL OF THE DRIFT-DIFFUSION TRANSPORT OF CHARGE CARRIERS CONSIDERING RECOMBINATION IN LAYERS WITH FRACTAL STRUCTURE
Abstract
A study model of the drift-diffusion transport of charge carriers in the layers of fractal structure taking into account the process of recombination of charge carriers. In the closed form solutions are found model equations.
67-71