Zafar Rakhmonov

Zafar Rakhmonov
National University of Uzbekistan · Department of Applied Mathematics

Professor

About

14
Publications
1,120
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
40
Citations
Citations since 2016
14 Research Items
40 Citations
2016201720182019202020212022024681012
2016201720182019202020212022024681012
2016201720182019202020212022024681012
2016201720182019202020212022024681012
Additional affiliations
December 2019 - August 2021
National University of Uzbekistan
Position
  • Head of Department
Education
September 2004 - July 2011
National University of Uzbekistan
Field of study
  • Apllied mathematics

Publications

Publications (14)
Conference Paper
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...
Article
Full-text available
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...
Book
Full-text available
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...
Conference Paper
Full-text available
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...
Conference Paper
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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.

Network

Cited By