Alimardon

@mathinst.uz

Scientific Laboratory of Mathematical Modeling of Nonlinear Systems
V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan

Alimardon


               Download Compact PDF  
https://researchid.co/alimardon

EDUCATION

Education

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematical Physics, Applied Mathematics, Numerical Analysis, Modeling and Simulation
11

Scopus Publications

73

Scholar Citations

5

Scholar h-index

3

Scholar i10-index

Scopus Publications

  • A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model
    A. N. Elmurodov, N. Yuldoshev
    Uzbek Mathematical Journal, 2025
    In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing dichotomy; namely, as $t$ goes to infinity, both prey and predator successfully spread to the whole space and survive in the new environment, or they spread within a bounded area and eventually die out. The criteria governing spreading and vanishing are obtained.
  • A Free Boundary Problem for a Prey-Predator Model with Degenerate Diffusion and Predator-Stage Structure
    A. N. Elmurodov, A. I. Sotvoldiyev
    Lobachevskii Journal of Mathematics, 2025
    Abstract In this paper, we study a free boundary problem for a stage-structured predator-prey model with degenerate diffusion and advection terms. The predator species is classified into immature and mature stages, and the interaction with prey species is modeled using a reaction-diffusion system. Initially, the predator species occupies a bounded region, while the prey population is distributed throughout the spatial domain. The dynamics of the free boundary, which describes the spreading of the predator species, are governed by a Stefan-like condition involving the spatial gradient of the predator density. We establish the existence and uniqueness of classical solutions to the problem using a priori estimates in Holder spaces and the Leray–Schauder fixed-point principle. Furthermore, we analyze the asymptotic behavior of the free boundary and derive the minimal spreading speed for the predator population. Our results demonstrate key phenomena related to spreading and vanishing: If the predator’s initial habitat or movement rate is sufficiently large, it will dominate and successfully spread; In contrast, predators with smaller habitats or slower movement may vanish over time.
  • Predator-Prey Model with a Free Boundary
    Alimardon Elmurodov, Ibodat Khaldibaeva, Nurila Yuldoshev
    Aip Conference Proceedings, 2024
    In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type, which are necessary for the solvability of the problem are established. The predator v is the invader which exists initially in a sub-interval [0, s0] of [0, l] and has the Leslie–Gower terms that measure the loss in the predator population due to rarity of the prey. The prey u (the native species) is initially distributed over the whole region [0, l]. Uniqueness of the solution is shown and qualitative properties of the solution are investigated.
  • A Diffusive Leslie–Gower Type Predator–Prey Model with Two Different Free Boundaries
    A. N. Elmurodov, A. I. Sotvoldiyev
    Lobachevskii Journal of Mathematics, 2023
    Abstract In this paper, we study the diffusive mutualist model with advection and different free boundaries in one space dimension. These two free boundaries may intersect each other as time evolves and can be used to describe the spreading of invasive and native species directly. Methods for obtaining a priori estimates in the norms of Hölder spaces for the solution are proposed. On the basis of these estimates, the existence and uniqueness of the solution are proved. Then we provide the criteria governing spreading and vanishing. At last we investigate long time behaviors and asymptotic spreading speeds of two species and asymptotic speeds of two free boundaries.
  • Free boundary problem for predator-prey model
    Alimardon Elmurodov, Abduraxmon Norov, N. Yuldasheva, Sanjarbek Yuldashev, Mavjuda Sadullayeva
    E3s Web of Conferences, 2023
    In this article, we study the behavior of two species evolving in a domain with a free boundary. This system mimics the spread of invasive or new predator species, in which free boundaries represent the expanding fronts of predator species and are described by the Stefan condition. A priori estimates for the required functions are established. These estimates are used to prove the existence and uniqueness of the solution.
  • A Free Boundary Problem for a Predator-Prey System
    M. S. Rasulov, A. N. Elmurodov
    Lobachevskii Journal of Mathematics, 2023
    Abstract In this paper we consider a free boundary problem for a system of quasilinear parabolic equations of the reaction-diffusion type. Methods for obtaining a priori estimates in the norms of Hölder spaces for the solution are proposed. On the basis of these estimates, the existence and uniqueness of the solution are proved.
  • On the Free Boundary Problem for the Predator-Prey Model
    Alimardon Elmurodov, Muyassar Hidoyatova, Zardila Shakhobiddiova
    Aip Conference Proceedings, 2023
    \nIn this article, we study the behavior of two species evolving in a domain with a free boundary. This system mimics the spread of invasive or new predator species, in which free boundaries represent the expanding fronts of predator species and are described by the Stefan condition. A priori estimates for the required functions are established. These estimates are used to prove the existence and uniqueness of the solution.\n
  • On a Uniqueness of Solution for a Reaction-Diffusion Type System with a Free Boundary
    A. N. Elmurodov, M. S. Rasulov
    Lobachevskii Journal of Mathematics, 2022
    In this paper, the mixed two-phase Stefan problem for a system of reaction-diffusion equations is considered. The behavior of free boundaries is studied. A priori estimates of Schauder type are established, on the basis of which the unique solvability of the problem is proved.
  • A Leslie-Gower predator-prey model with a two-free boundary
    Alimardon Elmurodov, Nurilla Yuldashev, Rustam Maqsudov, Gulnoz Abdikayimova
    2022 International Conference on Information Science and Communications Technologies Icisct 2022, 2022
    In this article, we study the behavior of two species evolving in a domain with a two-free boundary. This system mimics the spread of invasive or new predator species, in which free boundaries represent the expanding fronts of predator species and are described by the Stefan condition. A priori estimates for the required functions are established. These estimates are used to prove the existence and uniqueness of the solution.
  • A reaction-diffusion-advection competition model with a free boundary
    Uzbek Mathematical Journal, 2021
    In this paper, we study a competitive diffusion quasilinear system with a free boundary. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type are established, which are necessary for the solvability of the problem. One of two competing species is an invader, which initially exists on a certain sub-interval. The other is initially distributed throughout the area under consideration. Examining the influence of baseline data on the success or failure of the first invasion. We conclude that there is a dichotomy of spread and extinction and give precise criteria for spread and extinction in this model.
  • About mathematical model with a free boundary of water basins pollutions
    Uzbek Mathematical Journal, 2020

RECENT SCHOLAR PUBLICATIONS

  • Mathematical Modeling of a Reaction-Diffusion System with a Free Boundary
    A Elmurodov, M Toshmuradova
    Journal of Osh University. Differential Equations, 24-38 , 2026
    2026
  • A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model
    AN Elmurodov, N Yuldoshev
    Uzbek Mathematical Journal 69 (4), 83-95 , 2025
    2025
  • A Free Boundary Problem for a Prey-Predator Model with Degenerate Diffusion and Predator-Stage Structure
    AI Elmurodov, A.N., Sotvoldiyev
    Lobachevskii J Math 46 (2), 647–657 , 2025
    2025
    Citations: 1
  • Predator-prey model with a free boundary
    E Alimardon, K Ibodat, Y Nurila
    AIP Conf. Proc. 3004 (040001), (2024) , 2024
    2024
  • A Diffusive Leslie–Gower Type Predator–Prey Model with Two Different Free Boundaries
    AN Elmurodov, AI Sotvoldiyev
    Lobachevskii Journal of Mathematics 44 (10), 4254-4270 , 2023
    2023
    Citations: 4
  • A free boundary problem for a Predator-Prey System
    MS Rasulov, AN Elmurodov
    Lobachevskii Journal of Mathematics 44 (7), 2898-2909 , 2023
    2023
    Citations: 6
  • МНОГОФАЗНЫЕ ЗАДАЧИ СО СВОБОДНОЙ ГРАНИЦЕЙ ДЛЯ СИСТЕМ ПАРАБОЛИЧЕСКИХ УРАВНЕНИЙ ТИПА РЕАКЦИЯ ДИФФУЗИЯ
    E Alimardon
    https://kengash.mathinst.uz/files/Dissertatsiya-avtoreferati-Elmurodov … , 2023
    2023
  • Multi-phase problems with a free boundary for systems of parabolic equations of the reaction-diffusion type
    A Elmurodov
    Toshkent , 2023
    2023
  • A Leslie-Gower predator-prey model with a two-free boundary
    A. Elmurodov, N. Yuldashev
    International Conference on Information Science and Communications … , 2023
    2023
  • Free boundary problem for predator-prey model
    A. Elmurodov, A. Norov
    E3S Web of Conferences, CONMECHYDRO - 2023 401 (04062), https://doi.org/10 … , 2023
    2023
  • On the free boundary problem for the predator-prey model.
    A. Elmurodov, M. Hidoyatova, Z. Shakhobiddinova
    AIP Conference Proceedings 2781 (020042), https://doi.org/10.1063/5.0156674 , 2023
    2023
  • Биологическая инвазия в модели хищник-жертва со свободной границей
    AN Elmurodov
    Традиционная международная апрельская математическая 1 (2), 165-167 , 2023
    2023
  • On a uniqueness of solution for a reaction-diffusion type system with a free boundary
    AN Elmurodov, MS Rasulov
    Lobachevskii Journal of Mathematics 43 (8), 2099-2106 , 2022
    2022
    Citations: 14
  • A free boundary problem for a predator-prey model
    AN Elmurodov
    "Modern Materials Science: Topical Issues, Achievements and Innovations … , 2022
    2022
    Citations: 2
  • Simulation of pollution migration processes at municipal solid waste landfills
    AN Elmurodov
    Construction Mechanics, Hydraulics and Water Resources Engineering … , 2022
    2022
  • A Leslie-Gower predator-prey model with a two-free boundary
    AN Elmurodov
    International Conference on Information Science and Communications … , 2022
    2022
  • PREDATOR-PREY MODEL WITH A FREE BOUNDARY
    AN Elmurodov
    A B S T R A C T S INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE «MODERN … , 2022
    2022
    Citations: 3
  • A free boundary problem for a predator-prey competition model
    AN Elmurodov
    Programme of the international conference “сontemporary mathematics and its … , 2021
    2021
  • On the Free Boundary Problem for the Predator-Prey Model Journal of Physics: Conference Series
    A Elmurodov
    2021
  • Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection
    AN Elmurodov
    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki 36 (3), 110-122 , 2021
    2021
    Citations: 10

MOST CITED SCHOLAR PUBLICATIONS

  • On a uniqueness of solution for a reaction-diffusion type system with a free boundary
    AN Elmurodov, MS Rasulov
    Lobachevskii Journal of Mathematics 43 (8), 2099-2106 , 2022
    2022
    Citations: 14
  • A reaction-diffusion-advection competition model with a free boundary
    D Asrakulova, AN Elmurodov
    Uzbek Mathematical Journal 65 (3), 25-37 , 2021
    2021
    Citations: 12
  • Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection
    AN Elmurodov
    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki 36 (3), 110-122 , 2021
    2021
    Citations: 10
  • A free boundary problem for a Predator-Prey System
    MS Rasulov, AN Elmurodov
    Lobachevskii Journal of Mathematics 44 (7), 2898-2909 , 2023
    2023
    Citations: 6
  • On a mathematical model with a free boundary for water basin pollution
    JO Takhirov, AN Elmurodov
    Uzbek Mathematical Journal 2020 (4), 44-57 , 2020
    2020
    Citations: 6
  • The two-phase Stefan problem for parabolic equations
    AN Elmurodov
    Uzbek Mathematical Journal 2019 (4), 56-67 , 2019
    2019
    Citations: 5
  • A Diffusive Leslie–Gower Type Predator–Prey Model with Two Different Free Boundaries
    AN Elmurodov, AI Sotvoldiyev
    Lobachevskii Journal of Mathematics 44 (10), 4254-4270 , 2023
    2023
    Citations: 4
  • PREDATOR-PREY MODEL WITH A FREE BOUNDARY
    AN Elmurodov
    A B S T R A C T S INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE «MODERN … , 2022
    2022
    Citations: 3
  • A free boundary problem for a predator-prey model
    AN Elmurodov
    "Modern Materials Science: Topical Issues, Achievements and Innovations … , 2022
    2022
    Citations: 2
  • ДВУХФАЗНАЯ ЗАДАЧА СТЕФАНА ДЛЯ КВАЗИЛИНЕЙНЫХ ПАРАБОЛИЧЕСКИХ УРАВНЕНИЙ
    АН Элмуродов
    Актуальные проблемы науки и образования в современном ВУЗе, 189-193 , 2019
    2019
    Citations: 2
  • Трехфазная задача со свободной границей для уравнений типа реакция-диффузия
    АН Элмуродов
    Дифференциальные уравнения и математическое моделирование, 67-67 , 2019
    2019
    Citations: 2
  • Двухфазная задача со свободной границей для квазилинейных параболических уравнений
    АН Элмуродов
    ББК 22.251 я431+ 95.4 М341, 106-109 , 2019
    2019
    Citations: 2
  • Об одной задаче со свободной границей дляпараболического уравнения типа реакция-диффузия
    АН Элмуродов
    Актуальные проблемы прикладной математики, 290-290 , 2018
    2018
    Citations: 2
  • A Free Boundary Problem for a Prey-Predator Model with Degenerate Diffusion and Predator-Stage Structure
    AI Elmurodov, A.N., Sotvoldiyev
    Lobachevskii J Math 46 (2), 647–657 , 2025
    2025
    Citations: 1
  • The two-phase Stefan problem for quasilinear parabolic equations // Uzbek Mathematical Journal
    AN Elmurodov
    Uzbek Mathematical Journal 2019 (2), 39-48 , 2019
    2019
    Citations: 1
  • A two-phase free boundary problem for system of reaction-diffusion equations
    AN Elmurodov
    Uzbek Mathematical Journal 2018 (4), 58-72 , 2018
    2018
    Citations: 1
  • Mathematical Modeling of a Reaction-Diffusion System with a Free Boundary
    A Elmurodov, M Toshmuradova
    Journal of Osh University. Differential Equations, 24-38 , 2026
    2026
  • A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model
    AN Elmurodov, N Yuldoshev
    Uzbek Mathematical Journal 69 (4), 83-95 , 2025
    2025
  • Predator-prey model with a free boundary
    E Alimardon, K Ibodat, Y Nurila
    AIP Conf. Proc. 3004 (040001), (2024) , 2024
    2024
  • МНОГОФАЗНЫЕ ЗАДАЧИ СО СВОБОДНОЙ ГРАНИЦЕЙ ДЛЯ СИСТЕМ ПАРАБОЛИЧЕСКИХ УРАВНЕНИЙ ТИПА РЕАКЦИЯ ДИФФУЗИЯ
    E Alimardon
    https://kengash.mathinst.uz/files/Dissertatsiya-avtoreferati-Elmurodov … , 2023
    2023