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)
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卷 61, 编号 6 (2025)
ЛЮДИ НАУКИ
REVAZ VALERIANOVICh GAMKRELIDZE
Differencial'nye uravneniya. 2025;61(6):723
723
ORDINARY DIFFERENTIAL EQUATIONS
ASYMPTOTICS OF THE SPECTRUM FOR A FOURTH-ORDER DIFFERENTIAL OPERATOR WITH A SPECTRAL PARAMETER IN TWO BOUNDARY CONDITIONS
摘要
We consider the spectral problem a the fourth-order differential operator on a unit interval. In this case, two boundary conditions contain a spectral parameter. We assume that the coefficient of the differential expression is an absolutely continuous function. The main result is devoted to the sharp eigenvalue asymptotics at high energy. In addition, we obtain this result in the case of a smooth coefficient. This asymptotics shows an additional nonstandard effect, which is caused by the presence of a spectral parameter in the boundary conditions.
Differencial'nye uravneniya. 2025;61(6):724–738
724–738
PARTIAL DERIVATIVE EQUATIONS
SOLUTION OF THE CAUCHY PROBLEM FOR A HYPERBOLIC EQUATION WITH A NONLOCAL POTENTIAL
摘要
Using integral transformations, a solution to the initial value problem in a half-plane for a hyperbolic differential-difference equation with a translation in the free term along a spatial variable changing on the entire real axis is constructed in explicit form. It is proved that a solution to the problem exists if the real part of the symbol of the differential-difference operator in the equation is positive. Sufficient conditions for the coefficients and the shift of the equation are obtained, guaranteeing the existence of a solution to the problem.
Differencial'nye uravneniya. 2025;61(6):739–747
739–747
ON MULTIDIMENSIONAL EXACT SOLUTIONS OF GENERALIZED MONGE–AMPE`RE EVOLUTION EQUATIONS
摘要
We consider evolutionary multidimensional generalized Monge–Amp`ere equations, the right parts of which, in addition to the determinant of the Hesse matrix, may depend on the Laplace operator and the gradient of the desired function. A variant of the reduction method for constructing exact multidimensional solutions of the generalized Monge–Amp`ere evolution equations using separation of variables is proposed. Multivariate exact solutions expressed explicitly through elementary functions and through solutions of ordinary differential equations are obtained. A number of examples of exact solutions, both radially symmetric and anisotropic in spatial variables, expressed through combinations of elementary functions are given.
Differencial'nye uravneniya. 2025;61(6):748–762
748–762
CONSERVATIVE EQUATIONS IN FIELD THEORY — CONSERVATION AND SYMMETRY LAWS
摘要
The paper introduces a new class of field equations (in Minkowski space), which are called conservative equations. The distinctive features of the introduced equations are their symmetry with respect to transformations with the unitary group U(2) and the presence of additional conservation laws corresponding to the group U(2). A gauge invariant system of equations combining the conservative equation and the Yang–Mills equations is considered. It is proposed to use this system of equations to describe the dynamics of a neutrino with a nonzero mass interacting with the SU(2) Yang–Mills field (field of weak interactions).
Differencial'nye uravneniya. 2025;61(6):763–785
763–785
ON THE SOLVABILITY OF THE FIRST INITIAL-BOUNDARY VALUE PROBLEM FOR PARABOLIC SYSTEMS IN A BOUNDED DOMAIN WITH NON-SMOOTH LATERAL BOUNDARIES ON THE PLANE
摘要
The first initial-boundary value problem for Petrovskii second-order parabolic system in a bounded domain on the plane is investigated. The coefficients of the system satisfy the double Dini condition. The lateral boundaries of the domain admit cusps at the initial moment of time. The question of the existence of a solution to that problem in the space of functions that are continuous and bounded together with their highest derivatives in the closure of the domain is studied. An integral representation of that solution is obtained. Corresponding estimates are established.
Differencial'nye uravneniya. 2025;61(6):786–801
786–801
CONTROL THEORY
MODELLING THE DYNAMICS OF SOCIAL PROTESTS: MEAN-FIELD GAMES AND INVERSE PROBLEMS
摘要
In recent years, there has been an increase in social tension all over the world, which manifests itself in the form of social protests. Understanding the dynamics of street protests and studying the factors that can influence their occurrence, duration and intensity is crucial for the stable and sustainable development of society. One of the approaches to constructing various scenarios of social dynamics is to use the theory of mean-field games. A combined mathematical model of social protests based on the approach of mid-level games and dynamic systems is proposed. Numerical results of solving the inverse problem based on statistical data of the social movement in France for 2018–2019 are presented.
Differencial'nye uravneniya. 2025;61(6):802–822
802–822
NUMERICAL METHODS
ON SOME FORMULATIONS AND EXACT SOLUTIONS OF BOUNDARY VALUE PROBLEMS OF QUASI-ONE-DIMENSIONAL HEMODYNAMICS
摘要
A boundary value problem for quasi-one-dimensional hemodynamic equations for a straight circular vessel in which unsteady pressure and flow functions are set as a boundary condition is considered. The conditions for limited and unlimited solution existence, as well as existence of retrograde blood flow in the vessel, are formulated and proved.
Differencial'nye uravneniya. 2025;61(6):823–838
823–838
BRIEF MESSAGES
REPRESENTATION OF THE GREEN’S FUNCTION OF THE NAVIER PROBLEM FOR THE BIHARMONIC EQUATION IN A BALL
摘要
The paper presents a new representation of the Green’s function of the Navier problem for the biharmonic equation in the unit ball and gives a representation of the solution of the Navier problem for the homogeneous biharmonic equation without explicit use of the Green’s function.
Differencial'nye uravneniya. 2025;61(6):839–844
839–844
CHRONICLE
O SEMINARE PO KAChESTVENNOY TEORII DIFFERENTsIAL'NYKh URAVNENIY V MOSKOVSKOM GOSUDARSTVENNOM UNIVERSITETE IMENI M.V. LOMONOSOVA
摘要
Ниже публикуются краткие аннотации докладов, состоявшихся в весеннем семестре 2025 г. (предыдущее сообщение о работе семинара дано в журнале “Дифференциальные уравнения”. 2024. Т. 60. № 11)
Differencial'nye uravneniya. 2025;61(6):845-864
845-864