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Vol 61, No 8 (2025)
ORDINARY DIFFERENTIAL EQUATIONS
1011–1031
SINGULAR AND FIXED POINTS OF MAPPING GENERATED BY A MULTIDIMENSIONAL SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS WITH RELAY HYSTERESIS
Abstract
For a dynamical system described by a multidimensional system of ordinary differential equations with a two-position relay hysteresis, we have obtained the conditions for the mapping generated by this system, under which there exist singular and fixed points. We have established that in the case when a space is of even dimension, the existence of fixed mapping points is possible in the set of singular points.
Differential equations. 2025;61(8):1032-1040
1032-1040
On One Class of Periodic 𝐸-Functions
Abstract
It is shown that a periodic 𝐸-function whose derivatives at zero are integer algebraic numbers satisfies a differential equation of the form 𝑃(𝑦, 𝑦′) = 0 where 𝑃 is a polynomial with algebraic coefficients. Consequently, it is proven that every such function is a Laurent polynomial in an exponential 𝑒𝛼𝑧.
Differential equations. 2025;61(8):1041–1047
1041–1047
PARTIAL DERIVATIVE EQUATIONS
1048–1058
Solvability Criterion and Analytic Continuation of the Solution of the Cauchy Problem for the Biharmonic Equation in R3
Abstract
The question of the solvability of the problem of analytic continuation of the solution of the biharmonic equation in a spatial domain is considered, based on the values of the solution itself and its partial derivatives up to the third order given on a part of the boundary of the domain.
Differential equations. 2025;61(8):1059–1070
1059–1070
CONTROL THEORY
ON SUFFICIENT CONDITIONS FOR OPTIMALITY IN THE WEIGHT MINIMIZATION PROBLEM FOR A SHELL OF REVOLUTION AT A GIVEN VIBRATION FREQUENCY
Abstract
We consider shallow elastic shells with a given circular boundary and seek an axisymmetric shell shape minimizing the weight at a given fundamental frequency of shell vibrations. Using the obtained formula for the gradients of the components of the eigenfunction corresponding to the minimum eigenvalue, the second Frechet differentiability of the frequency functional is established. It is proved that when the necessary conditions are met, the sufficient conditions are also realized.
Differential equations. 2025;61(8):1071–1081
1071–1081
Stabilization of a Switched Interval System with Commensurate Delays Under Slow Switchings
Abstract
An approach is proposed to construct a digital controller that stabilizes a continuous switched linear interval system with commensurate delays in control under slow switchings. The stabilization approach consistently includes the construction of a switched continuously-discrete closed system with a digital controller, the transition to its discrete model, represented as a switched discrete linear interval system with modes of various orders, simultaneous stabilization of the subsystems of the resulting discrete model and the calculation of the delay time, ensuring the stability of the initial switched system, closed by the found controller.
Differential equations. 2025;61(8):1082–1093
1082–1093
Observability of Time-Varying Discrete Descriptor Systems
Abstract
Time-varying linear and nonlinear descriptor systems of observation with discrete time are considered. In the linear case, the criteria for observability on the finite horizon are obtained, and the conditions for robust observability are found. The duality theorems linking the properties of controllability and observability are proved. For nonlinear systems, the conditions of local observability on the finite horizon are obtained, using linear approximation.
Differential equations. 2025;61(8):1094–1116
1094–1116
NUMERICAL METHODS
CONSERVATIVE COMPACT AND MONOTONE FOURTH-ORDER DIFFERENCE SCHEMES FOR ONE-DIMENSIONAL AND TWO-DIMENSIONAL QUASILINEAR EQUATIONS
Abstract
Compact and monotone difference schemes of the fourth order of accuracy, preserving the property of conservatism (divergence) for the one-dimensional and two-dimensional quasilinear stationary reaction-diffusion equation are constructed and investigated. A priori estimates of the difference solution in the nonlinear case for the one-dimensional quasilinear equation are obtained based on the established two-sided estimates of the grid solution. For the linearization of the nonlinear difference scheme, an iterative method of the Newton-Seidel type is used, preserving conservatism and monotonicity. The main idea of the proposed difference schemes is based on the possibility of parallelizing the computational process. The emerging problems of finding additional boundary conditions at boundary nodes in both one-dimensional and two-dimensional cases are solved using the Newton interpolation polynomial of the fourth order of accuracy. The presented results of the computational experiments illustrate the increased order of the proposed algorithms. The possibility of generalizing this method to non-stationary quasilinear equations is also indicated.
Differential equations. 2025;61(8):1117-1134
1117-1134
BRIEF MESSAGES
Generalization of the oblique derivative problem for the Helmholtz equation in a disk
Abstract
A boundary value problem for the Helmholtz equation in a circle is considered, with the boundary condition containing an oblique derivative with Hölder coefficients. The solvability of the problem in a unique way is proved under certain restrictions on the parameter.
Differential equations. 2025;61(8):1135–1138
1135–1138
CHRONICLE
O SEMINARE PO PROBLEMAM NELINEYNOY DINAMIKI I UPRAVLENIYa V MOSKOVSKOM GOSUDARSTVENNOM UNIVERSITETE IMENI M.V. LOMONOSOVA
Abstract
Ниже публикуются краткие аннотации докладов, состоявшихся в весеннем семестре 2025 г. (предыдущее сообщение о работе семинара дано в журнале “Дифференциальные уравнения”. 2025. Т. 61. № 2; дополнительная информация по адресу iline@cs.msu.ru
Differential equations. 2025;61(8):1139-1139
1139-1139