Differential Equations
The journal publishes articles and reviews, chronicles of scientific life, anniversary articles and obituaries.
Media registration certificate: № 0110211 от 08.02.1993
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.
Founders
- Russian Academy of Sciences;
- Department of Informatics, Computer Engineering and Automation RAS
Editor-in-Chief
- Sadovnichii Victor Antonovich, Academician RAS, Doctor of Sc.
Frequency / Assess
12 issues per year / Subscription
Included in
White List (1st level), Higher Attestation Commission List, RISC
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.
Current Issue
Open Access
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Vol 2, No 62 (2026)
ORDINARY DIFFERENTIAL EQUATIONS
On the Baire class of the lower Vinograd exponent considered as a function of a real parameter
Abstract
A parametric family of linear systems of differential equations with continuous and bounded coefficients, continuously dependent on a real parameter, is constructed such that the lower central Vinograd exponent of its systems is not a function of the second Baire class.
Differential Equations. 2026;2(62):147-154
147-154
PARTIAL DERIVATIVE EQUATIONS
Existence theorem for a weak solution of the feedback control problem for the Kelvin–Voigt model with a smoothed Jaumann time derivative
Abstract
The paper deals with the weak solvability of the fluid motion feedback control problem for the Kelvin-Voigt model with smoothed Jaumann time derivative. For the proof, the original problem is interpreted as an operator inclusion. Then, an approximation problem is considered for which solvability is established based on the degree theory of multivalued completely continuous vector fields and a priori estimates of solutions. Then, based on a priori estimates independent of the approximation parameter, it is shown that from the sequence of solutions of the approximation problem it is possible to extract a subsequence weakly converging to the solution of the original problem as the approximation parameter tends to zero. After which it is shown that among the solutions of the problem under study there is at least one solution that gives a minimum to the specified cost functional.
Differential Equations. 2026;2(62):155-174
155-174
Acoustic Tomography Problem with Memory
Abstract
The system of the acoustic equations in which the Lame parameter possesses a memory is considered. The dependence of the memory means that the physical process at a fixed moment of time is determined by the whole prehistory and it is described by the special integral operator, a kernel of which is a product of two functions. One of those functions depends on the space coordinates while the other function depends on time. A posing of the acoustic tomography problem is studied. In it three functions are recovered, namely, the speed of acoustic waves, a density of the medium and a component of the kernel which depends of spaced variables. For solving the posed problem, the information on a series of direct problems for the acoustic equation with point sources is used. This information is given for a finite time interval at points lying on a sphere, inside of which the recovered coefficients are assumed to be unknown. It is shown that the considered problem is reduced to the inverse kinematic problem for recovering the speed of waves and to two problems of X-ray tomography.
Differential Equations. 2026;2(62):175-185
175-185
HOMOGENIZATION OF THE RIEMANN–HILBERT PROBLEM FOR THE GENERALIZED BELTRAMI EQUATION WITH LOCAL BOUNDARY CONDITIONS
Abstract
The work is devoted to the averaging of one Riemann–Hilbert problem for the generalized Beltrami equation with local boundary conditions. The homogenization error estimates are obtained of the order O(pq ") (q > 2, " > 0 is a small parameter) with a constant q, depending only on the ellipticity constant and the domain Q.
Differential Equations. 2026;2(62):186-203
186-203
Existence of a Global Solution and Blow-Up of the Solution to the Cauchy Problem for the Nonlinear Mindlin–Hermann Equation of Longitudinal Rod Vibrations
Abstract
For a nonlinear partial differential equation of the fourth order in time, modeling the propagation of longitudinal waves in a rod, the Cauchy problem is investigated in the space of continuous functions defined on the entire numerical axis and for which limits at infinity exist. Conditions for the existence of a global solution and the blowup of a solution to the Cauchy problem on a finite time interval are considered.
Differential Equations. 2026;2(62):204-227
204-227
On the existence and nonexistence of solutions of a boundary value problem for a nonlinear hyperbolic system of the fourth order
Abstract
For a class of high-order nonlinear hyperbolic systems, a boundary value problem in a cylindrical domain with given Cauchy-type conditions on the lower and upper bases of the cylinder and Dirichlet and Robin-type conditions on part of its lateral surface is considered. Using methods of functional analysis, the boundary value problem is equivalently reduced to a nonlinear functional equation on a subspace of Sobolev space. Conditions on the nonlinear terms of the system are given, under which an a priori estimate of the solution to the boundary value problem is obtained, and the existence of this solution is proven, while if these conditions are violated, the absence of solutions is investigated. The uniqueness of the solution to the problem is investigated.
Differential Equations. 2026;2(62):228-241
228-241
CONTROL THEORY
On the exact global controllability of a semilinear evolutionary equation with a nonstationary unbounded operator
Abstract
For the Cauchy problem associated with a controlled semilinear evolutionary equation with an unbounded nonstationary (i.e., time-dependent) operator in a Hilbert space, sufficient conditions for exact controllability to a given terminal state (as well as to given intermediate states at intermediate times) on an arbitrarily fixed (without additional conditions) time interval are obtained. The Minty-Browder theorem and the chain technology of sequential continuation of the solution of the controlled system to intermediate states are used. As examples, the problems for the heat equation and the wave equation with nonstationary coefficients are considered.
Differential Equations. 2026;2(62):242-261
242-261
BRIEF MESSAGES
262-266
Behavior of Solutions of a Degenerate Ordinary Differential Equation with Increasing Spectral Parameter
Abstract
The article studies a degenerate ordinary differential equation of high order with some parameter. Estimates and asymptotic expansions of solutions of the equation are obtained for large values of the parameter. Examples are considered in the cases of second- and third- order equations.
Differential Equations. 2026;2(62):267-275
267-275
CHRONICLE
About the seminar on problems of nonlinear dynamics and control at Lomonosov Moscow State University
Differential Equations. 2026;2(62):276-288
276-288