najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-6-742-748najo-117Research ArticleMATHEMATICSМАТЕМАТИКАQualitative properties of the mathematical model of nonlinear cross-diffusion processesКачественные свойства математической модели нелинейных кросс-диффузионных процессовhttps://orcid.org/0000-0003-2471-4836МуминовС.MuminovS.

Sokhibjan Muminov

Bolkhovuz street 2, Khiva 220900

Khamid Alimjan street 14, Urgench 220100

sokhibjan.muminov@mamunedu.uzhttps://orcid.org/0000-0001-7556-8942АгарвалП.AgarwalP.

Praveen Agarwal

Ajman, UAE

Jaipur 303012

Jaipur-302029

praveen.agarwal@anandice.ac.inhttps://orcid.org/0000-0003-2154-4157МухамедиеваД.MuhamediyevaD.

Dildora Muhamediyeva – Department of Software of Information Technologies

Amir Temur Avenue 108, Tashkent 100084

matematichka@inbox.ruMamun university; Urgench state universityUzbekistanNonlinear Dynamics Research Center (NDRC); Department of Mathematics, Anand International College of Engineering; International Center for Basic and Applied SciencesIndiaTashkent University of information technologies named after Muhammad Al-KhwarizmiUzbekistan202405062025156742748Copyright © Muminov S., Agarwal P., Muhamediyeva D., 20252025Муминов С., Агарвал П., Мухамедиева Д.Muminov S., Agarwal P., Muhamediyeva D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/117

The work is devoted to developing a self-similar solution for a system of nonlinear differential equations that describe diffusion processes. Various techniques are used to examine the capacity for generating self-similar solutions that can estimate and predict system behavior under diffusion conditions. The focus is on developing and applying numerical algorithms, as well as using theoretical tools such as asymptotic analysis, to obtain more accurate and reliable results. The study’s results can be applied to various scientific and technical fields, such as physics, chemistry, biology, and engineering, where diffusion processes play an essential role. The development of self-similar solutions for systems of nonlinear differential equations related to diffusion opens novel opportunities for modeling and analyzing complex systems and enhancing diffusion processes in various fields.

Работа посвящена разработке самоподобного решения для системы нелинейных дифференциальных уравнений, описывающих процессы диффузии. Различные методы используются для изучения возможности генерации самоподобных решений, которые могут оценивать и предсказывать поведение системы в условиях диффузии. Основное внимание уделяется разработке и применению численных алгоритмов, а также использованию теоретических инструментов, таких как асимптотический анализ, для получения более точных и надежных результатов. Результаты исследования могут быть применены в различных научных и технических областях, таких как физика, химия, биология и инженерия, где процессы диффузии играют существенную роль. Разработка самоподобных решений для систем нелинейных дифференциальных уравнений, связанных с диффузией, открывает новые возможности для моделирования и анализа сложных систем и улучшения процессов диффузии в различных областях.

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The authors declare that there are no conflicts of interest present.