# Vol 62, No (2016)

**Year:**2016**Articles:**10**URL:**https://journals.rudn.ru/CMFD/issue/view/1593

## Full Issue

## Articles

5-18

### Stationary Solutions of Vlasov Equations for High-temperature Two-component Plasma

#### Abstract

We consider the rst mixed problem for the Vlasov-Poisson equations in in nite cylinder. This problem describes evolution of density of distribution for ions and electrons in a high-temperature plasma in the presence of an outer magnetic eld. We construct stationary solutions of the Vlasov-Poisson system of equations with the trivial potential of the self-consistent electric eld describing two-component plasma in in nite cylinder such that their supports are located in a distance from the boundary of the domain.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:19-31

19-31

### Physical Interpretation of a Mathematical Strict Solution for the Di raction Problem by Means of Heuristic Formulas

#### Abstract

We propose a new approach to constructing heuristic formulas describing the solution of the di raction problem. The formulas are based on physical principles and allow one to interpret the results of the mathematical strict solution. Since the heuristic formulas possess high performance and accuracy, they can also be used along with any strict approaches or experimental results for signi cant improvement of e ciency of solution of practical problems related to applications of the di raction theory.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:32-52

32-52

### Spectral Analysis of Integrodi erential Equations in a Hilbert Space

#### Abstract

We investigate the correct solvability of initial-value problems for abstract integrodi erential equations with unbounded operator coe cients in a Hilbert space. We do spectral analysis of operatorfunctions describing symbols of such equations. These equations are an abstract form of linear integrodi erential partial derivative equations arising in the viscoelasticity theory and having some other important applications. We establish the localization and the spectrum structure of operator-functions describing symbols of these equations.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:53-71

53-71

### On Behavior of Solutions of Parabolic Nondivergent Equations with Increasing Higher-Order Coe cients at Large Values of Time

#### Abstract

We investigate su cient conditions of stabilization to zero for solutions of the Cauchy problem for linear parabolic second-order equation with increasing higher-order coe cients and initial-value functions of power growth rate at in nity.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:72-84

72-84

### On Coercivity of Di erential-Di erence Equations with Incommensurable Shifts of Arguments

#### Abstract

Изучаются краевые задачи на ограниченных областях для дифференциально-разностных уравнений с несоизмеримыми сдвигами аргументов в старших членах. Получены условия равномерной относительно сдвигов аргументов сильной эллиптичности таких уравнений.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:85-99

85-99

### Domain of Existence of Solutions in the Optimal Control Problem for a Spacecraft with Limited Thrust

#### Abstract

We consider several most common optimal control problems for a low-thrust spacecraft. We investigate the existence of solutions for these problems. In the model with limited thrust, we use the numerical approach for construction of the domain of existence. As examples, we consider interplanetary transfers Earth-Mars and Earth-Mercury.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:100-123

100-123

### Traces of Generalized Solutions of Elliptic Di erential-Di erence Equations with Degeneration

#### Abstract

The paper is devoted to di erential-di erence equations with degeneration in a bounded domain Q ⊂ Rn. We consider di erential-di erence operators that cannot be expressed as a composition of a strongly elliptic di erential operator and a degenerated di erence operator. Instead of this, operators under consideration contain several degenerated di erence operators corresponding to di erentiation operators. Generalized solutions of such equations may not belong even to the Sobolev space W12(Q). Earlier, under certain conditions on di erence and di erentiation operators, we had obtained a priori estimates and proved that the orthogonal projection of the generalized solution onto the image of the di erence operator preserves certain smoothness inside some subdomains Qr ⊂ Q (Ur Qr = Q) instead of r the whole domain. In this paper, we prove necessary and su cient conditions in algebraic form for existence of traces on some parts of boundaries of subdomains Qr.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:124-139

124-139

### Coercive Solvability of Nonlocal Boundary-Value Problems for Parabolic Equations

#### Abstract

In a Banach space E we consider nonlocal problem v'(t) + A(t)v(t) = f(t) (0 0). We prove the coercive solvability of the problem in the Banach space C0α,α([0, 1], E) (0 < α < 1) with the weight (t + τ )α. This result was previously known only for a constant operator. We consider applications in the class of parabolic functional di erential equations with transformation of spatial variables and in the class of parabolic equations with nonlocal conditions on the boundary of domain. Thus, this describes parabolic equations with nonlocal conditions both in time and in spatial variables.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:140-151

140-151

### On the Convergence Rate of Continuous Newton Method

#### Abstract

In this paper, we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.

**Contemporary Mathematics. Fundamental Directions**. 2016;62:152-165

152-165