The article investigates the asymptotics of self-similar solutions of a nonlinear system of cross-diffusion with nonlocal boundary conditions and a source. The main results of the work include obtaining the leading term of the asymptotics of self-similar solutions and proposing a method for selecting the optimal initial approximation for the iterative process necessary for the numerical investigation of the problem. The asymptotic concepts and methods presented in the article lend significance to the theory of combustion, particularly in the analysis of reactions occurring during combustion. Given that the rate of chemical reaction strongly depends on temperature, the asymptotic approach can be useful for modeling such processes. Additionally, numerical calculations and analysis of results were conducted using asymptotic formulas as initial approximations for the iterative process. This approach allows for a more efficient and accurate solution to the problem under consideration. Overall, the article makes an important contribution to understanding and modeling combustion processes using asymptotic methods and numerical calculations.
| Mualliflar | Урунбаев, Ж.Э. |
|---|---|
| Jurnal | Рақамли технологияларнинг назарий ва амалий масалалари |
| Nashriyot | ТАТУ Самарқанд филиали |
| ISSN | 2181-3086, 2181-3094 |
| Nashr sanasi | 2024-04-09 |
| Jild | 7 |
| Son | 1 |
| Betlar | 102-106 |
| Til | Ingliz |
| Ilmiy soha | Texnika |
| DOI | 10.62132/ijdt.v7i1.170 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.62132/ijdt.v7i1.170 · Maqolaning asl sahifasi
cross-diffusion, critical exponents, global existence, unbounded solutions, self-similar analysis, кросс диффузия, критические экспоненты, глобального существование, неограниченные решения, автомодельный анализ
| APA | Урунбаев, Ж.Э. (2024). Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source. Рақамли технологияларнинг назарий ва амалий масалалари, 7(1), 102-106. https://doi.org/10.62132/ijdt.v7i1.170 |
|---|---|
| GOST (OAK) | Урунбаев, Ж.Э. Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source // Рақамли технологияларнинг назарий ва амалий масалалари. – 2024. – T. 7, № 1. – P. 102-106. – DOI: 10.62132/ijdt.v7i1.170. |
| MLA | Урунбаев, Ж.Э. “Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source.” Рақамли технологияларнинг назарий ва амалий масалалари, 7(1), 102-106, 2024. https://doi.org/10.62132/ijdt.v7i1.170 |
| Chicago | Урунбаев, Ж.Э. “Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source.” Рақамли технологияларнинг назарий ва амалий масалалари, 7(1), 102-106 (2024). https://doi.org/10.62132/ijdt.v7i1.170 |
| Harvard | Урунбаев, Ж.Э (2024) ‘Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source’, Рақамли технологияларнинг назарий ва амалий масалалари, 7(1), 102-106. https://doi.org/10.62132/ijdt.v7i1.170 |
| BibTeX | @article{article2024,
title = {Numerical Solution of the Cross-Diffusion Problem with Nonlocal Boundary Conditions and a Source},
author = {Урунбаев, Ж.Э.},
journal = {Рақамли технологияларнинг назарий ва амалий масалалари},
year = {2024},
volume = {7},
number = {1},
pages = {102-106},
doi = {10.62132/ijdt.v7i1.170},
url = {https://doi.org/10.62132/ijdt.v7i1.170}
} |
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