Zafar Rakhmonov

National University of Uzbekistan · Department of Applied Mathematics

The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the ef...

Actual problems of applied mathematics and information technologies - Al-Khwarizmi 2024: abstracts of the international scientific conference (22-23 October 2024, Tashkent, Uzbekistan). – Tashkent. 2024.

The article is devoted to the study of economic cycles within the framework of the theory of Kondratieff's long waves or K-waves. The object of the study is Dubovsky's fractional mathematical models, which consist of two nonlinear ordinary differential equations of fractional order and describe the dynamics of the efficiency of new technologies and...

We study the global solvability and unsolvability of a nonlinear diffusion system with nonlinear boundary conditions in the case of slow diffusion. We obtain the critical exponent of the Fujita type and the critical global existence exponent, which plays a significant part in analyzing the qualitative characteristics of nonlinear models of reaction...

This paper presents a parallel corpus of raw texts between the Uzbek and Kazakh languages as a dataset for machine translation applications, focusing on the data collection process, dataset description, and its potential for reuse. The dataset-building process includes three separate stages, starting with a tiny portion of already available paralle...

In this paper, we study the global solvability and unsolvability of a nonlinear diffusion system with nonlinear boundary conditions in the case of slow diffusion. The conditions for the global existence of the solution in time and the unsolvability of the solution of the diffusion problem in a homogeneous medium are found on the basis of comparison...

The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of a fractional variable order of the Riemann–Liouville type. The issues of stability and convergence of an implicit finite-difference scheme are considered. Test examples are given to substantiate the theoretical results. Using the Runge rule, the...

In this paper, we study the global solvability and unsolvability of one nonlinear system of non-Newtonian polytropic filtration with a nonlocal boundary condition in the case of slow diffusion. We are constructed various self-similar solutions to the nonlinear filtration problem in the slow diffusion case. The conditions for the global existence of...

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benetti...

The book of abstracts contains the brief description of talks of the participants of the international conference ”Contemporary mathematics and its application”. The topics are related to mathematical modelling of nonlinear processes, algebra and functional analysis, differential equations and dynamical systems, ill-posed and inverse problems, ma...

The book of abstracts contains the brief description of talks of the participants of the international conference " Modern problems of applied mathematics and information technologies al-Khwarizmi 2021". The topics are related to the scientific heritage of Al-Khwarizmi, theory of algorithms, mathematical modeling of nonlinear processes, algebra and...

In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponent...

Microseismic phenomena are studied by a Sel'kov generalized nonlinear dynamic system. This system is mainly applied in biology to describe substrate and product glycolytic oscillations. Thus, Sel'kov dynamic system can also describe interaction of two types of fractures in an elastic-friable medium. The first type includes seed fractures with lower...

Mathematical models of nonlinear cross diffusion are described by a system of nonlinear partial parabolic equations associated with nonlinear boundary conditions. Explicit analytical solutions of such nonlinearly coupled systems of partial differential equations are rarely existed and thus, several numerical methods have been applied to obtain appr...

In this paper, based on a self-similar analysis and the method of standard equations, the properties of a nonlinear cross-diffusion system coupled via nonlocal boundary conditions are studied. We are investigated the qualitative properties of solutions of a nonlinear system of parabolic equations of crossdiffusion in a medium coupled with nonlinear...

In this paper, we study the asymptotic behavior of self-similar solutions of a nonlinear system of cross diffusion coupled via nonlocal boundary conditions. The main term of the asymptotics of self-similar solutions is obtained. For the numerical investigation of the problem is provided a method of selecting suitable initial guess for the iterative...

Condition of global existence of solution of a non-linear system of cross-diffusion with non-linear boundary conditions is studied in the paper. Critical exponents of Fujita type and critical exponents of global existence of solution are established

In this paper, we study the asymptotic behavior of self-similar solutions of a nonlinear cross-diffusion system coupled in the nonlocal boundary conditions. On the basis of selfsimilar analysis the main term of the asymptotics of self-similar solutions is obtained. A numerical scheme is constructed based on the finite difference method. For this, e...

The conditions of global existence of solutions of a nonlinear filtration problem in an inhomogeneous medium are investigated in this paper. Various techniques such as the method of standard equations, self-similar analysis and the comparison principle are used to obtain results. The influence of inhomogeneous medium on the evolution process is ana...

In this paper we study the global solvability and no solvability conditions of a multidimensional nonlinear problem of non-Newtonian filtration with nonlocal boundary condition in the slow diffusion case. Establish the critical global existence exponent and critical Fujita exponent of nonlinear filtration problem in inhomogeneous medium, which play...

In this paper we study the global solvability or nosolvability of a nonlinear filtration problem with nonlinear flux boundary condition in the fast diffusion case. The critical global existence and critical Fujita exponent by constructing various self-similar supersolutions and subsolutions are obtained.