Analysis of a density-dependent multidimensional cross-diffusion model with nonlinear boundary conditions

Rakhmonov, Zafar, Urunbaev, Jasur, Joniev, Akmal

Innovative Multidisciplinary Journal of Applied Technology · 2025-yil

Annotatsiya

Recently, the cross-diffusion problem has gained importance in solving problems of mathematical modelling of complex processes such as population dynamics, diffusion in multiphase media and reaction-diffusion systems and therefore has attracted considerable attention. Studies have shown that cross-diffusion elements in models can significantly change the qualitative and quantitative properties of solutions. However, many aspects of solutions, especially nonlinear boundary value problems, have not been sufficiently studied, which requires further and more in-depth study of these issues and creates the need for a more in-depth theoretical analysis. Based on the above considerations, the objective of this study is to formulate and analyse the scientific problem associated with the dynamic behaviour of the cross-diffusion problem based on the conditions of existence and non-existence of a global solution and the influence of boundary and parametric conditions on solutions based on self-similar analysis. The research methodology is based on the use of a self-similar approach, which allows simplifying the system of differential equations by introducing variables that are invariant with respect to changes in measurements. The main conclusion of the work is that the use of self-similar variables not only significantly simplifies the study of complex cross-diffusion models but also allows us to obtain important information about the stability limits of solutions.

Maqola ma’lumotlari
MualliflarRakhmonov, Zafar, Urunbaev, Jasur, Joniev, Akmal
JurnalInnovative Multidisciplinary Journal of Applied Technology
NashriyotТДТУ Қўқон филиали
ISSN2995-486X, 2995-486x
Nashr sanasi2025-10-28
Jild3
Son10
Betlar128-132
TilIngliz
DOI10.51699/pc7z5g80
Indeksga qo‘shilgan2026-08-26

DOI: 10.51699/pc7z5g80 · Maqolaning asl sahifasi

Kalit so‘zlar

self-similar analysis nonlinear parabolic system, cross-diffusion, diffusion, critical exponents of the Fujita type, blow-up, existence, non-existence

Iqtibos keltirish

APARakhmonov, Zafar, Urunbaev, Jasur, & Joniev, Akmal (2025). ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS. Innovative Multidisciplinary Journal of Applied Technology, 3(10), 128-132. https://doi.org/10.51699/pc7z5g80
GOST (OAK)Rakhmonov, Zafar, Urunbaev, Jasur, Joniev, Akmal ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS // Innovative Multidisciplinary Journal of Applied Technology. – 2025. – T. 3, № 10. – P. 128-132. – DOI: 10.51699/pc7z5g80.
MLARakhmonov, Zafar, Urunbaev, Jasur, and Joniev, Akmal. “ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS.” Innovative Multidisciplinary Journal of Applied Technology, 3(10), 128-132, 2025. https://doi.org/10.51699/pc7z5g80
ChicagoRakhmonov, Zafar, Urunbaev, Jasur, and Joniev, Akmal. “ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS.” Innovative Multidisciplinary Journal of Applied Technology, 3(10), 128-132 (2025). https://doi.org/10.51699/pc7z5g80
HarvardRakhmonov, Zafar, Urunbaev, Jasur, and Joniev, Akmal (2025) ‘ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS’, Innovative Multidisciplinary Journal of Applied Technology, 3(10), 128-132. https://doi.org/10.51699/pc7z5g80
BibTeX
@article{rakhmonovzafar2025,
  title = {ANALYSIS OF A DENSITY-DEPENDENT MULTIDIMENSIONAL CROSS-DIFFUSION MODEL WITH NONLINEAR BOUNDARY CONDITIONS},
  author = {Rakhmonov, Zafar and Urunbaev, Jasur and Joniev, Akmal},
  journal = {Innovative Multidisciplinary Journal of Applied Technology},
  year = {2025},
  volume = {3},
  number = {10},
  pages = {128-132},
  doi = {10.51699/pc7z5g80},
  url = {https://doi.org/10.51699/pc7z5g80}
}

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