In this article, a system of parabolic equations with nonlinear boundary conditionsis transformed into a system of self-similar (automodel) equations by applying a shapeshifting. Anasymptotics for a compact supporting solution of the problem is proposed. The obtained asymptoticformulas are used as an initial approximation in the numerical solution of the problem. In numericalexperiments k = 3 is taken, a finite-difference scheme is proposed, and a Python program is developedto perform computations for various parameter values, corresponding graphs obtained.Numerical experiments have shown that the iterative processes converge within 3 to 5 steps. Thecompactly supported self-similar asymptotic solution used as the initial approximation played animportant role in ensuring the convergence of the iterative process. The graphs illustrate that, fordifferent numerical parameter values, the reaction–diffusion processes occur at a finite speed.
| Mualliflar | Rakhmonov, Zafar, Zaripova, Aziza |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 187-198 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-2-22 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-2-22 · Maqolaning asl sahifasi
System of nonlinear equations,, reaction-diffusion, global solution, asymptotic, numer- ical solution.
| APA | Rakhmonov, Zafar, & Zaripova, Aziza (2026). Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions. O‘zbekiston matematika jurnali, 70(2), 187-198. https://doi.org/10.29229/uzmj.2026-2-22 |
|---|---|
| GOST (OAK) | Rakhmonov, Zafar, Zaripova, Aziza Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 187-198. – DOI: 10.29229/uzmj.2026-2-22. |
| MLA | Rakhmonov, Zafar, and Zaripova, Aziza. “Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions.” O‘zbekiston matematika jurnali, 70(2), 187-198, 2026. https://doi.org/10.29229/uzmj.2026-2-22 |
| Chicago | Rakhmonov, Zafar, and Zaripova, Aziza. “Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions.” O‘zbekiston matematika jurnali, 70(2), 187-198 (2026). https://doi.org/10.29229/uzmj.2026-2-22 |
| Harvard | Rakhmonov, Zafar, and Zaripova, Aziza (2026) ‘Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions’, O‘zbekiston matematika jurnali, 70(2), 187-198. https://doi.org/10.29229/uzmj.2026-2-22 |
| BibTeX | @article{rakhmonovzafar2026,
title = {Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions},
author = {Rakhmonov, Zafar and Zaripova, Aziza},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {2},
pages = {187-198},
doi = {10.29229/uzmj.2026-2-22},
url = {https://doi.org/10.29229/uzmj.2026-2-22}
} |
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