Vol 239, No 6 (2019)
- Year: 2019
- Articles: 10
- URL: https://journals.rcsi.science/1072-3374/issue/view/15010
Article
Stationary Solutions of the Vlasov Equations for a High-Temperature Two-Component Plasma
Abstract
We consider the first mixed problem for the Vlasov–Poisson equations in infinite cylinder. This problem describes evolution of the distribution density for ions and electrons in a high-temperature plasma in the presence of an outer magnetic field. We construct stationary solutions of the Vlasov–Poisson system of equations with the trivial potential of the self-consistent electric field describing a two-component plasma in an infinite cylinder such that their supports are located at a distance from the boundary of the domain.
Physical Interpretation of Strict Solutions of Diffraction Problems by Heuristic Relations
Abstract
We propose a new approach to construct heuristic relations describing solutions of diffraction problems. Those relations are based on physical principles and allow one to interpret mathematically strict solutions. Since the heuristic relations possess high performance and accuracy, they can also be used along with any strict approach or experimental results for a significant improvement of efficiency of solutions of practical problems related to applications of the diffraction theory.
Spectral Analysis of Integrodifferential Equations in Hilbert Spaces
Abstract
We investigate the well-posedness of initial-value problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space and provide the spectral analysis of operator-functions describing symbols of such equations. These equations are an abstract form of linear partial integrodifferential equations arising in the viscoelasticity theory and other important applications. We establish the localization and the spectrum structure of operator-functions describing symbols of these equations.
On Large-Time Behavior of Solutions of Parabolic Nondivergent Equations with Increasing Principal Coefficients
Abstract
We investigate sufficient conditions of the stabilization to zero for solutions of the Cauchy problem for linear parabolic second-order equations with increasing principal coefficients and initial-value functions growing at infinity as a power function.
On Coercivity of Differential-Difference Equations with Incommensurable Translations of Arguments
Abstract
Boundary-value problems in bounded domains are studied for differential-difference equations with incommensurable translations of independent variables in principal terms. Conditions of the uniform (with respect to translations of independent variables) strong ellipticity of such equations are obtained.
Existence Domain for Solutions of Optimal Control Problems for Bounded-Thrust Spacecrafts
Abstract
We consider several of the most common optimal-control problems for low-thrust spacecrafts. We investigate the existence of solutions for those problems. For the bounded-thrust model, we use the numerical approach to construct the existence domain. As examples, we consider the Earth–Mars and Earth–Mercury interplanetary flights.
Traces of Generalized Solutions of Elliptic Differential-Difference Equations with Degeneration
Abstract
This paper is devoted to differential-difference equations with degeneration in a bounded domain Q ⊂ ℝn. We consider differential-difference operators that cannot be expressed as a composition of a strongly elliptic differential operator and a degenerated difference operator. Instead of this, the operators under consideration contain several degenerate difference operators corresponding to differential operators. Generalized solutions of such equations may not belong even to the Sobolev space \( {W}_2^1(Q) \).
Earlier, under certain conditions on the difference and differential operators, we obtained a priori estimates and proved that, instead of the whole domain, the orthogonal projection of the generalized solution to the image of the difference operator preserves certain smoothness inside some subdomains \( {Q}_r\subset Q\left(\underset{r}{\mathrm{U}}{\overline{Q}}_r=\overline{Q}\right) \).
In this paper, we prove necessary and sufficient conditions in algebraic form for the existence of traces on parts of boundaries of subdomains Qr.
Coercive Solvability of Nonlocal Boundary-Value Problems for Parabolic Equations
Abstract
In an arbitrary Banach space E, we consider the nonlocal problem
for an abstract parabolic equation with a linear unbounded strongly positive operator A(t) such that its domain D = D(A(t)) is independent of t and is everywhere dense in E. This operator generates an analytic semigroup exp{−sA(t)}(s ≥ 0).
We prove the coercive solvability of the problem in the Banach space \( {C}_0^{\alpha, \alpha}\left(\left[0,1\right],E\right)\left(0<\alpha <1\right) \) with weight (t + τ)α. Earlier, this result was known only for constant operators. We consider applications in the class of parabolic functional differential equations with transformation of spatial variables and in the class of parabolic equations with nonlocal conditions on the boundary of the domain. Thus, this describes parabolic equations with nonlocal conditions both with respect to time and with respect to spatial variables.
On the Convergence Rate of the Continuous Newton Method
Abstract
In this paper we study the convergence of the continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on recent progress in the geometric theory of spiral-like functions. We prove convergence theorems and illustrate them by numerical simulations.