Main Article Content
In this work we considered a parabolic system of two quasilinear reaction-diffusion equations for a biological population problem of the Kolmogorov-Fisher type describes the process of a biological population in a nonlinear two-component medium. We studied the qualitative properties of the solution to Cauchy problem based on self-similar analysis and its numerical solutions using the methods of modern computer technologies, to study the methods of linearization to the convergence of the iterative process with further visualization.
- 1. A.V.Martynenko, A.F.Tedeev, The Cauchy problem for a quasilinear parabolic equation with a source and no homogeneous density, Comput. Math. Math. Phys. 47, 2007, no. 2, pp. 238–248.
- 2. M.Aripov, Sh.Sadullaeva, To properties of the equation of reaction diffusion with double nonlinearity and distributed parameters, Journal of Siberian Federal University. Mathematics & Physics, 2013, Vol. 6, Issue 2, pp 157–167.
- 3. Sh.Sadullaeva, Numerical Investigation of Solutions to a Reaction-diffusion System with Variable Density, Journal of Siberian Federal University. Mathematics & Physics, 9(1), 2016, pp. 90-101.
- 4. S.A.Sadullaeva, A.T.Khaydarov, F.A.Kabilianova, Modeling of Multidimensional Problems in Nonlinear Heat Conductivity in Non-Divergence Case, 3rd International Symposium on Multidisciplinary Studies and Innovative Technologies, ISMSIT 2019 – Proceedings, 8932954.
- 5. S.A.Sadullaeva, M.B.Khojimurodova, Properties of solutions of the cauchy problem for degenerate nonlinear cross systems with convective transfer and absorption, Springer Proceedings in Mathematics and Statistics, 264, 2018, pp. 183-190.
- 6. M.Aripov, S.Sadullaeva, An asymptotic analysis of a self-similar solution for the double nonlinear reaction-diffusion system, J. Nanosyst. Phys. Chem. Math., 2015, 6 (6), pp. 793-802.
- 7. M.Aripov, S. Sadullaeva, Qualitative properties of solutions of a doubly nonlinear reaction-diffusion system with a source, J. Appl. Math. Phys., 2015, 3, pp. 1090-1099.
- 8. D.K.Muhamediyeva, The property of the problem of reaction diffusion with double nonlinearity at the given initial conditions, International Journal of Mechanical and Production Engineering Research and Development, Volume 9, Issue 3, 2019, IJMPERDJUN2019117, Pages 1095-1106.
- 9. A.Mersaid, The fujita and secondary type critical exponents in nonlinear parabolic equations and systems, Springer Proceedings in Mathematics and Statistics, 2018, 268, pp. 9-23.
- 10. D.K.Muhamediyeva, Properties of self similar solutions of reaction-diffusion systems of quasilinear equations, International Journal of Mechanical and Production Engineering Research and Development, 8 (2), 2018, pp. 555-566.
- 11. S.A. Sadullaeva, G. Pardaeva, Numerical Investigation one System Reaction-Diffusion with Double Nonlinearity, Journal of Mathematics, Mechanics and Computer Science, 2018, 86 (3), 58-62.
- 12. M.Aripov, O.Djabbarov, Sh.Sadullaeva, Mathematic modeling of processes describing by double nonlinear parabolic equation with convective transfer and damping, AIP Conference Proceedings 2365, 060008 (2021); https://doi.org/10.1063/5.0057492
- 13. M.Aripov, S.Sadullaeva, N.Iskhakova, Numerical Modeling Wave Type Structures in Nonlinear Diffusion Medium with Dumping, 4th International Symposium on Multidisciplinary Studies and Innovative Technologies, ISMSIT 2020 - Proceedingsthis link is disabled, 2020, 9254988
- 14. S.Sadullaeva, Z.Fayzullaeva, D.Nazirova, Numerical Analysis of Doubly Nonlinear Reaction-Diffusion System with Distributed Parameters, 4th International Symposium on Multidisciplinary Studies and Innovative Technologies, ISMSIT 2020 - Proceedingsthis link is disabled, 2020, 9255106
- 15. A.Nematov, E.S.Nazirova, R.T.Sadikov, On numerical method for modeling oil filtration problems in piecewise-inhomogeneous porous medium, IOP Conference Series: Materials Science and Engineeringthis link is disabled, 2021, 1032(1), 012018
- 16. E.Nazirova, A.Nematov, R.Sadikov, I.Nabiyev, One-Dimensional Mathematical Model and a Numerical Solution Accounting Sedimentation of Clay Particles in Process of Oil Filtering in Porous Medium, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)this link is disabled, 2021, 12615 LNCS, стр. 353–360
- 17. N.Ravshanov, E.S.Nazirova, V.M.Pitolin, Numerical modelling of the liquid filtering process in a porous environment including the mobile boundary of the oil-water section, Journal of Physics: Conference Seriesthis link is disabled, 2019, 1399(2), 022021
- 18. S.Anarova, S.Ismoilov, Nonlinear mathematical model of stress-deformed state of spatially loaded rods with account for temperature, AIP Conference Proceedingsthis link is disabled, 2021, 2365, 070019
- 19. S.A.Anarova, S.M.Ismoilov, O.S.Abdirozikov, Software of Linear and Geometrically Non-linear Problems Solution Under Spatial Loading of Rods of Complex Configuration, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)this link is disabled, 2021, 12615 LNCS, стр. 380–389