Eurasian Mathematical Journal

On some geometric aspects of evolution variational problems

V.M. Filippov — 2025-09-30

The main objective of the work is to identify the relationship between evolution equations with potential operators and geometries of related configuration spaces of the given systems. Using the Hamilton principle, a wide class of such equations is derived. Their structural analysis is carried out, containing operator analogues of the Christoffel symbols of both the 1st and 2nd kind. It is shown that the study of the obtained evolution equations can be associated, in general, with an extended configuration space, the metric of which is determined by the kinetic energy of the given system.

Oscillatory and spectral analysis of higher-order differential operators

A. Kalybay — 2025-09-30

In the paper there are investigated the oscillatory properties of a 2nth order differential equation and the spectral properties of a 2nth order differential operator. These properties are established using the variational method, which relies on verifying a specific nth order differential inequality. Here, the coefficients of both the equation and the operator are the weights in this inequality. Furthermore, the characterization of the inequality occurs when the weights satisfy conditions, ensuring the existence of a certain combination of boundary values at infinity and at zero for the function involved in this inequality.

Algebras of binary formulas for weakly circularly minimal theories with equivalence relations

B.Sh. Kulpeshov — 2025-09-30

Algebras of binary isolating formulas are described for \(\aleph_0\)-categorical 1-transitive non-primitive weakly circularly minimal theories of convexity rank greater than 1 with a trivial definable closure, having only equivalence relations.

Reconstruction of the weighted differential operator with point \(\delta\)-interaction

M.Dzh. Manafov — 2025-09-30

In this article, we provide various uniqueness results for inverse problems of weighted differential operator with point \(\delta\)–interaction. In terms of the method of spectral mappings, we also offer step by step strategies for finding their potential and boundary conditions basing either on the Weyl function, on spectral data, or on two spectra.

Exact solution to a Stefan-type problem for a generalized heat equation with the Thomson effect

T.A. Nauryz — 2025-09-30

We study a one-dimensional Stefan type problem which models the behavior of electromagnetic fields and heat transfer in closed electrical contacts that arises, when an instantaneous explosion of the micro-asperity occurs. This model involves vaporization, liquid and solid zones, in which the temperature satisfies a generalized heat equation with the Thomson effect. Accounting for the nonlinear thermal coefficient, the model also incorporates temperature-dependent electrical conductivity. By employing a similarity transformation, the Stefan-type problem is reduced to a system of coupled nonlinear integral equations. The existence of a solution is established using the fixed point theory in Banach spaces.

Asymptotics of solutions of the Sturm-Liouville equation in vector-function space

Ya.T. Sultanaev — 2025-09-30

In this paper, we study the asymptotic behaviour of fundamental systems of solutions to the Sturm-Liouville equation with rapidly oscillating potentials in a two-dimensional vector-function space. We consider different cases in which the coefficients do not satisfy the regularity conditions. Additionally, we investigate the asymptotic behaviour of solutions in resonance cases.

Online workshop on differential equations and function spaces, dedicated to the 80-th anniversary of D.Sc., Professor Mikhail L'Vovich Goldman

Viktor Burenkov — 2025-09-30

Online workshop on differential equations and function spaces, dedicated to the 80-th anniversary of D.Sc., Professor Mikhail L'Vovich Goldman