Articles | Open Access | DOI: https://doi.org/10.37547/supsci-ojpm-04-03-01

MATHEMATICAL MODELING OF THE BIOLOGICAL POPULATION PROCESS WITH CONVECTIVE TRANSPORT

M. Aripov , National University of Uzbekistan named after Mirzo Ulugbek Tashkent, Uzbekistan
M. Sayfullaeva , Tashkent University of Information Technologies named after Muhammad al-Khorazmi Tashkent, Uzbekistan
F. Kabiljonova , National University of Uzbekistan named after Mirzo Ulugbek Tashkent, Uzbekistan

Abstract

In this article we will discuss one problem of a nonlinear biological population, with double nonlinearity; an exact analytical solution has been found for it, the analysis of which makes it possible to identify a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects were established: the inertial effect of the finite speed of population spread, spatial localization.

Keywords

biological population, model, front

References

Aripov M. Abdullaeva Z., On the bottom of the exact solution of a nonlinear problem with absorption or a source. Bulletin of the TATU, №4 2016, 107-113.

Wang M., Wei Y. Blow-up properties for a degenerate parabolic system with nonlinear localized sources // J. Math. Anal. Appl. 343 ,2008, p.621- 635.

Raimbekov J.R. The Properties of the Solutions for Cauchy Problem of Nonlinear Parabolic Equations in Non-Divergent Form with Density // Journal of Siberian Federal University. Mathematics & Physics 2015, 8(2), p.192-200.

Aripov M., Sadullayeva Sh., To properties of solutions to reaction diffusion equation with double nonlinearity with distributed parameters”, Jour. of Siberian Fed. Univer. Math. & Phys. 6, 2013, pp. 157-167.

Зельдович Я.Б., Райзер Ю.П. Физика ударных волн и высокотемпературных гидродинамических явлений // Изд. 2-е, доп. — М.: Наука, 1966, 688 с.

Aripov M., Sayfullayeva M. Problems of the biological population in a non-divergent form, Ilm sarchashmalari 8, 2020, pp.14–19

Aripov M., Sayfullayeva M. and Kabiljanova F., Exact solution of a double nonlinear problem of biological population with absorption and with migration, in 2021 International Conference on Information Science and Communications Technologies (ICISCT) (IEEE, 2021) pp. 1–4

Aripov M., Sayfullayeva M., Kabiljanova F., Bobokandov M., About one exact solution to the nonlinear problem of a biological population with absorption in a heterogeneous medium, AIP Conf. Proc. 3085, 020031, 2024.

Будянский А.В., Цибулин В.Г., Моделирование пространственно-временной миграции близкородственных популяции, Компьютерные исследования и моделирование, 2011, том 3, №.4, с.477-488.

Zhou WS, Wu ZQ: Some results on a class of degenerate parabolic equations not in divergence form. Nonlinear Anal. 60, 2005, pp. 863-886

Yao ZA, Zhou WS: Some results on a degenerate and singular diffusion equation. Acta Math. Sin. Ser. B 27, 2007, pp.581-601

Zhou WS: Some notes on a nonlinear degenerate parabolic equation. Nonlinear Anal. 71, 2007, pp.107-111

Wang J: Behaviors of solutions to a class of nonlinear degenerate parabolic equations not in divergence form. Appl. Math. Lett. 24, 2011, pp.191-195

Мартинсон Л.К., Нелинейные эффекты в процессе эволюции тепловых структур, // Ж. вычисл. матем. и матем. физ., 1984, том 24, №3, с.462–467.

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M. Aripov, M. Sayfullaeva, & F. Kabiljonova. (2024). MATHEMATICAL MODELING OF THE BIOLOGICAL POPULATION PROCESS WITH CONVECTIVE TRANSPORT. Oriental Journal of Physics and Mathematics, 4(03), 1–19. https://doi.org/10.37547/supsci-ojpm-04-03-01