Differencial'nye uravneniya
The journal publishes articles and reviews, chronicles of scientific life, anniversary articles and obituaries.
The journal is aimed at mathematicians, scientists and engineers who use differential equations in their research, at teachers, graduate students and students of natural science and technical faculties of universities and universities.
The journal is peer-reviewed and is included in the List of the Higher Attestation Commission of Russia for publishing works of applicants for academic degrees, as well as in the RISC system.
The journal was founded in 1965.
ISSN (print): 0374-0641
Media registration certificate: № 0110211 от 08.02.1993
Founder: Department of Informatics, Computer Science and Automation of the Russian Academy of Sciences, Russian Academy of Sciences (RAS)
Editor-in-Chief: Sadovnichii Victor Antonovich, Member of RAS, Doctor Phys.-Math. Sciences, Rector of Lomonosov Moscow State University
Number of issues per year: 12
Indexation: RISC, Higher Attestation Commission list, RISC core, RSCI, White list (1st level)
Current Issue
Open Access
Access granted
Subscription Access
Vol 61, No 1 (2025)
ЛЮДИ НАУКИ
K VOS'MIDESYaTIPYaTILETIYu NIKOLAYa ALEKSEEVIChA IZOBOVA
Differencial'nye uravneniya. 2025;61(1):3-4
3-4
PARTIAL DERIVATIVE EQUATIONS
MODEL PROBLEM IN A STRIP FOR THE HYPERBOLIC DIFFERENTIAL-DIFFERENCE EQUATION
Abstract
The paper investigates the question of the existence of a classical solution to the initial value problem with incomplete initial data on the boundary of the strip for a hyperbolic differential-difference equation. The equation contains a superposition of a differential operator and a translation operator with respect to a spatial variable that varies along the entire real axis. Using the Gelfand–Shilov operational scheme, a solution to the problem was obtained in explicit form.
Differencial'nye uravneniya. 2025;61(1):5-12
5-12
INSTABILITY AND STABILIZATION OF SOLUTIONS OF A STOCHASTIC MODEL OF VISCOELASTIC FLUID DYNAMICS
Abstract
The instability and stability of solutions of the stochastic system describing the flow of a viscoelastic liquid are investigated. It is shown that for certain values of the parameters included in the equations of the system, the existence of unstable and stable invariant spaces. For unstable case, the stabilization problem is solved based on the feedback principle.
Differencial'nye uravneniya. 2025;61(1):13-21
13-21
EXISTENCE OF SOLUTIONS OF THE BOUNDARY VALUE PROBLEM FOR THE DIFFUSION EQUATION WITH PIECEWISE CONSTANT ARGUMENTS
Abstract
In this paper the boundary value problem (BVP) for diffusion equation with piecewise constant arguments is studied. By using the separation of variables method, the considered BVP is reduced to the investigation of the existence conditions of solutions of initial value problems for differential equation with piecewise constant arguments. Existence conditions of infinitely many solutions or emptiness for considered differential equation are established and explicit formula for these solutions are obtained. Several examples are given to illustrate the obtained results.
Differencial'nye uravneniya. 2025;61(1):22-34
22-34
ON FRONT MOTION IN THE REACTION–DIFFUSION–ADVECTION PROBLEM WITH KPZ-NONLINEARITY
Abstract
We obtain an asymptotic approximation to a moving inner layer (front) solution of an initial– boundary value problem for a singularly perturbed parabolic reaction–diffusion–advection equation with KPZnonlinearity. An asymptotic approximation for the velocity of the front is found. To prove the existence and uniqueness of a solution the asymptotic method of differential inequalities is used.
Differencial'nye uravneniya. 2025;61(1):35-49
35-49
DIRICHLET PROBLEM FOR A TWO-DIMENSIONAL WAVE EQUATION IN A CYLINDRICAL DOMAIN
Abstract
In this work, the first boundary value problem is studied for a two-dimensional wave equation in a cylindrical domain. A uniqueness criterion has been established. The solution is constructed as the sum of an orthogonal series. When justifying the convergence of a series, the problem of small denominators from two natural arguments arose for the first time. An estimate for separation from zero with the corresponding asymptotics was established, which made it possible to prove the convergence of the series in the class of regular solutions and the stability of the solution.
Differencial'nye uravneniya. 2025;61(1):50-67
50-67
BLOW-UP OF THE SOLUTION AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR THE EQUATION OF VIBRATIONS OF A HOLLOW ROD
Abstract
For a nonlinear partial differential equation of Sobolev type, generalizing the equation of oscillations of a hollow flexible rod, the Cauchy problem is studied in the space of continuous functions defined on the entire numerical axis and for which there are limits at infinity. The conditions for the existence of a global classical solution and the blow-up of the solution to the Cauchy problem on a finite time interval are considered.
Differencial'nye uravneniya. 2025;61(1):68-83
68-83
INTEGRAL EQUATIONS
ON THE SOLVABILITY OF A SYSTEM OF MULTIDIMENSIONAL INTEGRAL EQUATIONS WITH CONCAVE NONLINEARITIES
Abstract
The work is devoted to the study of questions of existence and uniqueness of a continuous bounded and positive solution to one system of nonlinear multidimensional integral equations. The scalar analogue of the indicated system of integral equations, with different representations of the corresponding matrix kernel and nonlinearities, has important applied significance in a number of areas of physics and biology. This article proposes a special iterative approach for constructing a positive continuous and bounded solution to the system under study. It is possible to prove that the corresponding iterations uniformly converge to a continuous solution of the specified system. Using some a priori estimates for strictly concave functions, we also prove the uniqueness of the solution in a fairly wide subclass of continuous bounded and coordinately nonnegative vector functions. In the case when the integral of the matrix kernel has a unit spectral radius, it is proved that in a certain subclass of continuous bounded and coordinate-wise non-negative vector functions, this system has only a trivial solution, which is an eigenvector of the kernel integral matrix.
Differencial'nye uravneniya. 2025;61(1):84-98
84-98
CONTROL THEORY
STABLE SOLUTION OF PROBLEMS OF TRACKING AND DYNAMICAL RECONSTRUCTION UNDER MEASURING PHASE COORDINATES AT DISCRETE TIME MOMENTS
Abstract
The problem of dynamic reconstruction of input actions in a system of ordinary differential equations and the problem of tracking a trajectory of a system by some trajectory of another one influenced by an unknown disturbance are under consideration. An input action is assumed to be an unbounded function, namely, an element of the space of square integrable functions. Two solving algorithms, which are stable with respect to informational noises and computational errors and oriented to program realization, are designed. Upper estimates of their convergence rates are established. The algorithms are based on constructions from feedback control theory. They operate under conditions of (inaccurate) measuring the phase states of the given systems at discrete times.
Differencial'nye uravneniya. 2025;61(1):99-115
99-115
ON THE PROBLEM OF PURSUING A GROUP OF COORDINATED EVADERS IN A GAME WITH FRACTIONAL DERIVATIVES
Abstract
In a finite-dimensional Euclidean space, the problem of pursuing of a group of evaders by a group of pursuers is considered, described by a linear non-stationary system of differential equations with fractional Caputo derivatives. Sets of admissible players’ controls — compacts, terminal sets — origin of coordinates. Sufficient conditions have been obtained for the capture of at least one evader and all evaders under the condition that the evaders use the same control. In the study, the method of matrix and scalar resolving functions is used as a basic one. It is shown that differential games described by equations with fractional derivatives have properties that are different from those of differential games described by ordinary differential equations.
Differencial'nye uravneniya. 2025;61(1):116-132
116-132
BRIEF MESSAGES
BASS–GURA FORMULA FOR LINEAR SYSTEM WITH DYNAMIC OUTPUT FEEDBACK
Abstract
In this paper we solve the problem of assigning the desired characteristic polynomial of a linear stationary dynamic system with one input and output dynamic feedback in the form of a first-order dynamic compensator. Necessary and sufficient conditions for the existence of the solution of the problem are considered. An explicit formula for the compensator parameters, analogous to the Bass–Gura formula for a state feedback system, is derived.
Differencial'nye uravneniya. 2025;61(1):133-138
133-138
139-144