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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Том 61, № 10 (2025)
ORDINARY DIFFERENTIAL EQUATIONS
ULTIMATE DYNAMICS OF A CANCER MODEL WITH ANGIOGENIC SWITCH AND COMBINED THERAPY
Аннотация
The properties of the ultimate dynamics of one 5D model of cancer tumor growth in the angiogenesis phase with additional modeling of chemotherapy and immunotherapy are considered. The ultimate upper bounds for all cell populations, as well as the lower bound for the immune cell population, are found. The conditions for global asymptotic eradication of the tumor are obtained in two situations: when only chemotherapy is used and when a combination of chemotherapy and immunotherapy is used. The study is based on the method of localization of compact invariant sets. The article also describes the boundary and internal equilibrium points and presents the results of numerical simulation illustrating the results obtained analytically.
Differencial'nye uravneniya. 2025;61(10):1299-1315
1299-1315
ON THE WANDERING VELOCITY OF SOLUTIONS TO LINEAR AUTONOMOUS DIFFERENTIAL SYSTEMS
Аннотация
The wandering velocities of linear homogeneous differential systems with constant coefficients are studied. The accuracy of the wandering velocities is established on the set of solutions of autonomous differential systems. The principal values of the wandering velocity of the autonomous system are found; they coincide with the set of modules of the imaginary parts of the eigenvalues of the system matrix.
Differencial'nye uravneniya. 2025;61(10):1316-1325
1316-1325
PARTIAL DERIVATIVE EQUATIONS
ON SMOOTHNESS OF SOLUTION TO THE CAUCHY PROBLEM FOR A PARABOLIC EQUATION WITH DINI CONTINUOUS COEFFICIENTS
Аннотация
We consider the Cauchy problem for a spatially multidimensional second-order parabolic equation with Dini continuous coefficients. The initial function belongs to the class of continuous and bounded functions with uniformly continuous and bounded first-order spatial derivatives, the right-hand side of the equation can grow in a certain way when approaching the plane of the initial data. Using the Poisson potential and the volume potential, the smoothness of the solution to this problem is investigated and estimates of the solution and its first-order spatial derivatives are obtained.
Differencial'nye uravneniya. 2025;61(10):1326-1339
1326-1339
DARBOUX-TYPE PROBLEMS FOR A THIRD-ORDER HYPERBOLIC EQUATION WITH TWO INDEPENDENT VARIABLES
Аннотация
Sufficient conditions for the unique solvability of problems for a third-order hyperbolic equation with conditions on the characteristic and non-characteristic lines are obtained. Solutions to the problems are constructed in terms of a function analogous to the Riemann-Hadamard function.
Differencial'nye uravneniya. 2025;61(10):1340-1351
1340-1351
ON THE UNIQUE SOLVABILITY OF INITIAL-BOUNDARY VALUE PROBLEMS FOR PARABOLIC SYSTEMS IN A PLANE BOUNDED DOMAIN WITH GENERAL BOUNDARY CONDITIONS
Аннотация
An initial boundary value problem is considered for an inhomogeneous parabolic system with continuous coefficients with a nonzero initial condition in a plane bounded domain with nonsmooth lateral boundaries allowing the presence of “beaks” on which boundary conditions of the general form are set for the components of the desired vector function. Theorems on the existence and uniqueness of the classical solution of the problem from the space of vector functions that are continuous with their spatial derivative of the first order in the closure of the domain are proved. An integral representation is given, and the smoothness of the obtained solution is investigated.
Differencial'nye uravneniya. 2025;61(10):1352-1368
1352-1368
THE CAUCHY PROBLEM FOR A NONLINEAR HIROTA-TYPE EQUATION WITH A SELF-CONSISTENT SERIES SOURCE
Аннотация
In this paper the inverse spectral problem method is applied to integrate a nonlinear Hirota-type equation with a self-consistent series source in the class of periodic infinite-gap functions. An infinite system of differential equations is derived that describes the evolution of spectral data for the periodic Dirac operator. The solvability of the Cauchy problem for this system in the class of six times continuously differentiable periodic infinite-gap functions is proved. In addition, an algorithm for finding infinite-gap solution of the Cauchy problem for a Hirota-type equation with a self-consistent series source is proposed, and an exact solution is found in the case of the single-gap case for the Dirac operator.
Differencial'nye uravneniya. 2025;61(10):1369-1386
1369-1386
INTEGRAL EQUATIONS
STABILITY OF SOLUTIONS OF LINEAR FUNCTIONAL-INTEGRAL ITO EQUATIONS
Аннотация
The paper is devoted to the study of stability of solutions of a new class of linear functionally integral Itô equations, which contains many classical equations, e.g., differential equations of integer and fractional order with and without stochastic perturbations them, as well as some less known and understudied types of equations that have been introduced into scientific circulation recently. The connection between different types of stability of solutions of these equations and belonging of their solutions to the corresponding spaces of random processes. Using this connection sufficient conditions of stability of solutions with respect to initial data in terms of parameters of these equations. The notion of admissibility of pairs of spaces for the above mentioned the notion of admissibility of pairs of spaces for the above mentioned equations and the relationship between admissibility of pairs of spaces and stability with respect to the initial function.
Differencial'nye uravneniya. 2025;61(10):1387-1404
1387-1404
CONTROL THEORY
TRIAXIAL STABILIZATION OF A RIGID BODY VIA DELAYED FEEDBACK LAW
Аннотация
Two approaches to the problem of triaxial stabilization of a rigid body with the aid of delayed feedback law are considered. The first approach is based on the choosing control as a sum of dissipative and restoring torques with a constant delay in the restoring torque. In this case, to derive exponential stability conditions of program mode, a special construction of Lyapunov–Krasovskii functional is used. In the second approach, a control is constructed without using a dissipative torque. The stabilization is ensured via artificial introducing a delay in the restoring torque, and the proof of the exponential stability is based on the application of the Razumikhin method.
Differencial'nye uravneniya. 2025;61(10):1405-1415
1405-1415
FINITE STABILIZATION BASED ON INCOMPLETE MEASUREMENTS OF NOT COMPLETELY CONTROLLED SYSTEMS OF NEUTRAL TYPE
Аннотация
For linear autonomous differential-difference systems of neutral type, a solution to the problem of finite stabilization is proposed based on measurements of the observed output signal. A method for designing a corresponding controller whose structure does not contain links with distributed delay has been developed, and a criterion for its existence has been proven. The constructiveness of the results is illustrated by an example. A distinctive feature of the work is the possibility of finite stabilization of a class of systems that do not have the property of complete 0-controllability.
Differencial'nye uravneniya. 2025;61(10):1416-1440
1416-1440