Vol 206 (2022)
Статьи
On smoothing the operator coefficient of a first-order differential operator in a Banach space
Abstract
In this paper, we consider a first-order differential operator acting in Lebesgue spaces. The method of similar operators allows one to reduce the operator considered to an operator with a more convenient potential.
3-14
On a discrete equation in a quarter-plane and a related boundary-value problem
Abstract
Discrete equations of the convolution type in a quarter-plane are considered. We prove that each such equation is equivalent to an analog of the two-dimensional periodic Riemann problem on the torus. We describe sufficient conditions for the unique solvability of such a periodic Riemann problem and, as a consequence, conditions for the unique solvability of a discrete equation in terms of the symbol of the convolution operator.
15-22
Mathematical modeling of some aeroelastic systems
Abstract
In this paper, we develop mathematical models of a class of aerohydroelastic systems, namely, vibrating devices intended for intensification of technological processes. The dynamic stability of elastic components of these devices is examined. The notion of stability of a deformable body accepted in this paper coincides with the concept of the Lyapunov stability of dynamical systems. The models considered are governed by coupled nonlinear partial differential systems. The impact of a gas or fluid (in the model of an ideal medium) is determined from the asymptotic equations of aerohydromechanics. For describing the dynamics of elastic elements, we use the nonlinear theory of solid deformable bodies, which takes into account transverse and longitudinal deformations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals. Sufficient conditions for the stability of solutions of the systems proposed are obtained.
23-34
The law of conservation of electric charge and the physical interpretation of the generalized Cauchy-Riemann system
Abstract
In this paper, we continue the study of generalizations of the Cauchy-Riemann (CR) conditions obtained earlier, which, under certain assumptions, can be interpreted as Maxwell’s equations of electromagnetic field. The main mathematical tools used in the work is the technique of two quaternion variables. This work does not contain any physical statements, but is a theoretical analysis that can be carried out for systems of generalized CR conditions.
35-41
On a Neumann-type problem for the Burgers equation in a degenerate corner domain
Abstract
Using a priori estimates, the Faedo—Galerkin method, and other methods of functional analysis, we prove the well-posedness of the boundary-value problem for the Burgers equation with nonlinear Neumann-type boundary conditions in degenerate corner domains in Sobolev spaces.
42-62
On a nonlinear boundary-value problem for a third-order partial differential equations
Abstract
In this paper, we examine the existence of a solution to a nonlinear boundary-value problem for a third-order partial differential equation and propose an algorithm for the search for an approximate solution.
63-67
On the inverse problem of determining the lowest coefficient depending on the space variable in a parabolic equation with weak degeneracy
Abstract
In this paper, we prove existence and uniqueness theorems for solutions of the inverse problem of determining the x-dependent absorption coefficient in a degenerate parabolic equation. As an additional condition, the integral observation condition is specified. Also, we give examples of inverse problems satisfying the conditions of the theorems proved in the paper.
68-81
On the solvability of a fractional loaded heat conduction problem
Abstract
In this paper, we study a boundary-value problem for the loaded fractional heat equation; the loaded term is represented as the fractional Caputo derivative with respect to the time derivative.
82-97
On some models in linguistics
Abstract
Two diffusion models of language change are considered. The first model is an initialboundary-value problem for the Hotelling equation. This model describes the change in the size of a natural language vocabulary over time under the influence of its development and diffusion penetration. The other model describes the process of interaction between native speakers of two languages. The stability of stationary solutions is discussed.
98-106
On the statement and solvability of the l-problem of moments for fractional systems
Abstract
In this paper, we generalize the method of moments for optimal control problems for fractional linear systems with concentrated parameters to new types of systems. We analyze the statement and solvability of the l-problem of moments for the simplest one- and two-dimensional systems with Prabhakar, Saigo, and Grinko operators. In some cases, we obtain exact analytical solutions of this problem.
107-124
Integrability of lcACS-structures
Abstract
In this paper, we study almost Hermitian structures induced on maximal integral manifolds of the first fundamental distribution of a locally conformally almost cosymplectic manifold.
125-132
On the well-posedness of a model problem of heat and mass transfer in homogeneous semiconductor targets
Abstract
Based on the methods of the qualitative theory of differential equations, we examine the well-posedness of the mathematical model of one-dimensional diffusion of nonequilibrium charge carriers generated by an electron beam. We prove the continuous dependence of solutions on input data and obtain estimates of the influence of errors in the initial data on the distribution of the diffusing impurity. The results obtained can be used in electron probe technologies.
133-137
On one Dubinin problem for the weight capacitance of a Hesse condenser with A1-Mackenhaupt weight
Abstract
For the Hesse condenser in , n2, the equivalence of its weight capacitance and its weight modulus with A1-Muckenhoupt weight is proved. This gives a solution of the Dubinin problem on estimating the capacitance of a capacitor with the weight mentioned.
138-145