Vol 239 (2025)
Articles
Solution of a traveling-wave type to a mixed problem for a nonlinear system of first-order differential equations
Abstract
In this paper, we propose a solution of a traveling-wave type to a mixed problem for a nonlinear hyperbolic system of first-order partial differential equations with a modulus-type nonlinearity and obtain conditions for the existence of a solution of a traveling-wave type.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:3-12
3-12
The listing and counting combinatorial algorithm for compositions of a natural number with constraints
Abstract
In this paper, we propose a listing and counting algorithm for compositions of a natural number based on combinatorial objects of a hierarchical structure, such as Pascal's triangle, Pascal's pyramid, and Pascal's hyperpyramids. We obtain the recurrent relation that is the basis for listing and counting of compositions of a natural number with an arbitrary constraints on the values of its natural parts and the formula for explicit counting of compositions and a generating function for the number of compositions.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:13-24
13-24
Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie
Abstract
This article examines the minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. We obtain necessary conditions of equality type and inequality type for a strong as well as for a weak local minimum. Necessary conditions of equality and inequality types are obtained for strong as well as weak local minimum. A specific example demonstrating the effectiveness of the results in this paper is provided.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:25-31
25-31
Vortex models of shear laminar and turbulent flows
Abstract
We discuss a mathematical model of laminar and turbulent shear flows of liquids and gases in rectangular channels based on a system of differential equations describing the longitudinal motion and rotation of vortex tubes. We show that in the case of a plane steady flow, this system of equations has two-parameter analytical solutions for velocity distributions in the cross-section of the channel, which are in good agreement with known experimental data and the results of numerical simulations. Model approximations of velocity profiles of laminar flows of non-Newtonian liquids and developed turbulent flows of liquids and gases in rectangular channels are discussed as examples.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:32-42
32-42
Methods of boundary-value problems for improving control in systems with constraints
Abstract
In the class of state-nonlinear optimal control problems with constraints, a new approach to improving controls is proposed. This approach is based on solving special boundary-value problems by perturbation methods and parametrization of the optimal control problem by the perturbation parameter. The solution of the constructed unperturbed boundary-value problem is reduced to the solution of an algebraic equation for one unknown parameter. To solve the perturbed boundary-value problem, an iterative process is proposed, at each iteration of which a problem is solved that is similar in complexity to the unperturbed problem.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:43-52
43-52
Initial-boundary-value problems for some nonlinear mixed heat conductivity operators
Abstract
In this paper, we consider a computational model for a mixed nonlinear heat equation with boundary conditions of the third kind that describes the process of switching off an electric arc including the interval of its stable combustion until the moment of switching off and replacing the strictly hyperbolic heat equation with a hyperbolic-parabolic equation. The numerical simulation of this problem based on an implicit difference scheme and the heat balance method was performed by using the MathCad-15 software. Also, we prove the well-posedness of the first boundary-value problem for some high-order nonlinear equation.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:53-61
53-61
Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. IV. Ninth-order systems
Abstract
In this paper, we present new examples of integrable dynamical systems of the ninth order that are homogeneous in part of the variables. In these systems, subsystems on the tangent bundles of lower-dimensional manifolds can be distinguished. In the cases considered, the force field is partitioned into an internal (conservative) part and an external part. The external force introduced by a certain unimodular transformation has alternate dissipation; it is a generalization of fields examined earlier. Complete sets of first integrals and invariant differential forms are presented.The first part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 236 (2024), pp. 72–88.The second part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 237 (2024), pp. 49–75.The third part of the paper: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 238 (2024), pp. 69–100.
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory. 2025;239:62-97
62-97