Contemporary Mathematics. Fundamental Directions
type: channel
description: Editor-in-Chief: Alexander L. Skubachevskii, Professor, Doctor of Physical and Mathematical Sciences ISSN: 2413-3639 (print), 2949-0618 (online). Founded in 2003 г. Publication frequency: quarterly Open Access: . APC: no article processing charge Peer-Review: blind Publication language: Rus, Eng Indexation: White List, elibrary.ru, mathnet.ru, Google Scholar, DOAJ, Lens, Research4Life Publisher: Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)
publisher: Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)
language: ru-RU
publication name: Contemporary Mathematics. Fundamental Directions
issn: 2413-3639
copyright: The right of authorship belongs to the authors of articles. The authors transfer the rights to use the article (including the use and distribution of an article in the Open Access) to the publisher of the journal on a non-exclusive license (Publishing Agreement (Public Offer)). At the same time, authors remain full rightsholders. Publishing Agreement (Public Offer) to Publish an Article in an Academic Periodical "Contemporary Mathematics. Fundamental Directions" The Federal State Autonomous Educational Institution of Higher Education "Peoples’ Friendship University of Russia named after Patrice Lumumba” (RUDN University), represented by the Vice-Rector for Scientific Work Andrey Aleksandrovich Kostin, acting under a Power of Attorney No. 0036-03/21-163 dated 12.10.2021, hereinafter referred to as the Publisher, on the one hand, hereby offers to the public at large, hereinafter referred to as the Author, on the other hand, hereinafter collectively referred to as the Parties, to enter into this agreement, hereinafter referred to as the Agreement, regarding publication of scholarly materials, hereinafter referred to as the Article, in the Journal named 'Contemporary Mathematics. Fundamental Directions', hereinafter referred to as the Journal, under the following terms. 1. General Terms and Conditions 1.1. Pursuant to Clause 2 of the Article 437 of the Russian Federation Civil Code, this Agreement shall be recognized as the public offer, hereinafter referred to as the Offer. Subject to Article 438 of the Russian Federation Civil Code, this Offer shall be deemed to have been completely and irrevocably accepted after the Author had submitted his/her materials by uploading those onto the network electronic system of the article acquisition for review available at the respective section of the Journal's site at URL: http://journals.rudn.ru/index.php/CMFD/author/submit/1 on the Information and Communication Network known as the Internet, hereinafter referred to as the Intern…
items: Second-order difference scheme for hyperbolic equations with unbounded delay
items: A mathematical theoryof the accelerated expansion of the Universe based on the principle of least action
items: Parameterization of control functions in the problem of modeling HIV infection therapy
items: A study of the solvability of the Bingham alpha model
items: On the differential model of sandpiles growing in a silo
items: On the damping of a neutral-type control system on a temporal star graph with time-proportional delay
items: Dirac geometric structures
items: A class of anisotropic diffusion-transport equations in nondivergent form
items: Dynamics of the conformation tensor in viscoelastic FENE polymer models

Second-order difference scheme for hyperbolic equations with unbounded delay
type: item
description: The present paper is devoted to the study the initial value problem for the hyperbolic equation with unbounded time delay term \( \begin{equation*} \begin{cases} \dfrac{d^{2}v(t)}{dt^{2}}+A^{2}v(t)=a\left( \dfrac{dv(t-\omega )}{dt} +Av(t-\omega )\right) +f(t), & t>0, \\ v(t)=\varphi (t), & -\omega \leq t\leq 0 \end{cases} \end{equation*} \) in a Hilbert space H with a self-adjoint positive definite operator A. The second order of accuracy difference scheme for the numerical solution of the differential problem is presented. The main theorem on stability estimates for the solutions of this difference scheme is established. In practice, the stability estimates for solutions of four problems for hyperbolic difference equations with time delay are proved.
creator: A. Ashyralyev
rights: Copyright (c) 2025 Ashyralyev A. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 547
ending page: 561
doi: 10.22363/2413-3639-2025-71-4-547-561

A mathematical theoryof the accelerated expansion of the Universe based on the principle of least action
type: item
description: In classical works, the equations for gravitational and electromagnetism fields are proposed without deriving the right-hand sides. Here, we derive the right-hand sides and analyze the energy-momentum tensor within the framework of the Vlasov-Maxwell-Einstein equations and consider cosmological models such as Milne-McCrea and Friedmann. This allows us to place General Relativity (GR) on a rigorous mathematical foundation: to derive a closed system of GR equations from the principle of least action and provide a rigorous definition of cosmological solutions. This explains the accelerated expansion of the Universe without Einstein’s lambda, dark energy, or fantastic new fields, but as a simple relativistic effect.
creator: V. V. Vedenyapin
creator: Ya. G. Batishcheva
creator: M. V. Goryunova
creator: A. A. Russkov
rights: Copyright (c) 2025 Vedenyapin V.V., Batishcheva Y.G., Goryunova M.V., Russkov A.A. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 562
ending page: 584
doi: 10.22363/2413-3639-2025-71-4-562-584

Parameterization of control functions in the problem of modeling HIV infection therapy
type: item
description: Mathematical modeling is actively used to study the mechanisms of human immunodeficiency virus of type 1 (HIV-1) infection. Current HIV-1 therapy involves the regular, lifelong use of multiple antiviral drugs. However, this therapy is associated with varying degrees of side effects due to toxicity, drug interactions, resistance development, and high cost. Mathematical models of HIV-1 infection and optimal control methods can be used to develop effective regimens for applying multiple antiretroviral drugs, taking into account the immune status of HIV-1-infected patients. In this study, we identify the pharmacodynamic parameters of drugs based on a previously constructed stochastic model of the processes that determine viral replication in infected cells. We also study the efficiency of standard therapy for various HIV-1 infection regimens using a system dynamics model. The results of the study indicate the need to take into account differences in the body’s response to therapy based on the criterion of efficiency, which actualizes the task of selecting individual therapy regimens using optimal control methods based on physiologically approved models of HIV-1 infection.
creator: D. S. Grebennikov
creator: A. I. Lyfenko
creator: A. M. Timokhin
creator: R. S. Savinkov
creator: G. A. Bocharov
rights: Copyright (c) 2025 Grebennikov D.S., Lyfenko A.I., Timokhin A.M., Savinkov R.S., Bocharov G.A. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 585
ending page: 603
doi: 10.22363/2413-3639-2025-71-4-585-603

A study of the solvability of the Bingham alpha model
type: item
description: This article studies the solvability of the initial-boundary value problem for the alpha model of a Bingham-type viscoplastic fluid with periodic conditions on the spatial variables. Using an approximation-topological approach, we prove the existence of weak solutions to the alpha model under study and establish the convergence of the alpha model solutions to the solutions of the original model as the alpha parameter tends to zero.
creator: A. V. Zvyagin
creator: N. V. Tolstoy
rights: Copyright (c) 2025 Zvyagin A.V., Tolstoy N.V. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 604
ending page: 625
doi: 10.22363/2413-3639-2025-71-4-604-625

On the differential model of sandpiles growing in a silo
type: item
description: We discuss some features of a boundary value problem for a system of PDEs that describes the growth of a sandpile in a container under the action of a vertical source. In particular, we characterize the long-term behavior of the profiles, and we provide a sufficient condition on the vertical source that guarantees the convergence to the equilibrium in a finite time. We show by counterexamples that a stable configuration may not be reached in a finite time, in general, even if the source is timeindependent. Finally, we provide a complete characterization of the equilibrium profiles.
creator: Graziano Crasta
creator: Annalisa Malusa
rights: Copyright (c) 2025 Crasta G., Malusa A. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 626
ending page: 641
doi: 10.22363/2413-3639-2025-71-4-626-641

On the damping of a neutral-type control system on a temporal star graph with time-proportional delay
type: item
description: On a temporal star graph, we consider the problem of optimally damping a control system for a generalized pantograph equation, which is a neutral-type equation with time-proportional delay. The delay in the system propagates through an internal vertex of the graph. We study the variational problem of minimizing the energy functional, taking into account the probabilities of scenarios corresponding to different edges. We establish that the optimal trajectory satisfies Kirchhofftype conditions at the internal vertex. We prove the equivalence of the variational problem to a certain boundary-value problem for second-order functional differential equations on the graph, and establish the unique solvability of both problems.
creator: A. P. Lednov
rights: Copyright (c) 2025 Lednov A.P. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 642
ending page: 654
doi: 10.22363/2413-3639-2025-71-4-642-654

Dirac geometric structures
type: item
description: For Hamiltonian systems on symplectic manifolds with constraints in the Dirac model of generalized Hamiltonian dynamics, V. V. Kozlov considered the operation of symplectic projection of a Hamiltonian vector field for the case of generalized nonintegrable differential constraints. This paper considers a constraint regularization method that circumvents the degeneracy of the symplectic projection operation in the case of an odd number of constraints. The method is based on embedding of the original system into an extended system of higher dimension with an increased number of constraints.
creator: T. V. Salnikova
creator: E. I. Kugushev
rights: Copyright (c) 2025 Salnikova T.V., Kugushev E.I. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 655
ending page: 662
doi: 10.22363/2413-3639-2025-71-4-655-662

A class of anisotropic diffusion-transport equations in nondivergent form
type: item
description: We generalize Einstein’s probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected displacement per unit time with the velocity of the fluid, we derive an anisotropic diffusion equation in non-divergence form that contains a transport term. Under the Darcy law assumption, a corresponding nonlinear partial differential equations for the density function is obtained. The classical solutions of this equation are studied, and the maximum and strong maximum principles are established. We also obtain exponential decay estimates for the solutions for all time, and particularly, their exponential convergence as time tends to infinity. Our analysis uses some transformations of the Bernstein-Cole-Hopf type which are explicitly constructed even for very general equation of state. Moreover, the Lemma of Growth in time is proved and utilized in order to achieve the above decaying estimates.
creator: L. Hoang
creator: A. I. Ibragimov
rights: Copyright (c) 2025 Hoang L., Ibragimov A.I. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 663
ending page: 685
doi: 10.22363/2413-3639-2025-71-4-663-685

Dynamics of the conformation tensor in viscoelastic FENE polymer models
type: item
description: In this work, the equations for the dynamics of the invariants of the conformational tensor for FENE polymer solution models are derived and integrated. Explicit formulas for the invariants as functions of the time parameter along the trajectory of fluid particles are obtained. The invariants are represented as functions of the Lambert function. A description of the qualitative behavior of the invariants under different regimes is given.
creator: A. P. Chupakhin
creator: E. S. Stetsyak
creator: D. S. Chutkov
rights: Copyright (c) 2025 Chupakhin A.P., Stetsyak E.S., Chutkov D.S. https://creativecommons.org/licenses/by-nc/4.0
license: https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-25
publication date: 2025-12-25
volume: 71
number: 4
starting page: 686
ending page: 700
doi: 10.22363/2413-3639-2025-71-4-686-700