Critical thresholds and asymptotic behavior of weak solutions to nonlinear weighted coupled parabolic equations

A. U. Mamatov, I.O. Murodullayev

Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi · 2026-yil

Annotatsiya

This paper investigates the qualitative properties of weak solutions to a coupled system of nonlinear weighted parabolic equations featuring p-Laplacian diffusion and exponential reaction terms. By employing a self-similar scaling approach, we analyze the asymptotic behavior of solutions and derive the structural properties of the filtration process in multidimensional domains. We establish rigorous criteria for global-in-time existence and identify the critical thresholds for finite-time blow-up in the supercritical regime. It is shown that for initial data exceeding a specific critical parameter, the solution undergoes a blow-up in finite time. These analytical findings are validated through numerical simulations using the Peaceman-Rachford alternating direction implicit (ADI) scheme, which effectively captures the diffusion front evolution and localization effects. The results provide insights into the interplay between spatial weights and nonlinear coupling in degenerate parabolic systems.

Maqola ma’lumotlari
MualliflarA. U. Mamatov, I.O. Murodullayev
JurnalSamarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi
NashriyotСамарқанд давлат университети
ISSN2091-5446, 2181-1296
Nashr sanasi2026-07-01
Jild1
Son3
Betlar23-28
TilIngliz
DOI10.59251/2181-3973.2025.v1.138.1.3877
Indeksga qo‘shilgan2026-09-02

DOI: 10.59251/2181-3973.2025.v1.138.1.3877 · Maqolaning asl sahifasi

Iqtibos keltirish

APAA. U. Mamatov, & I.O. Murodullayev (2026). CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 23-28. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3877
GOST (OAK)A. U. Mamatov, I.O. Murodullayev CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2026. – T. 1, № 3. – P. 23-28. – DOI: 10.59251/2181-3973.2025.v1.138.1.3877.
MLAA. U. Mamatov, and I.O. Murodullayev. “CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 23-28, 2026. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3877
ChicagoA. U. Mamatov, and I.O. Murodullayev. “CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 23-28 (2026). https://doi.org/10.59251/2181-3973.2025.v1.138.1.3877
HarvardA. U. Mamatov, and I.O. Murodullayev (2026) ‘CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 23-28. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3877
BibTeX
@article{aumamatov2026,
  title = {CRITICAL THRESHOLDS AND ASYMPTOTIC BEHAVIOR OF WEAK SOLUTIONS TO NONLINEAR WEIGHTED COUPLED PARABOLIC EQUATIONS},
  author = {A. U. Mamatov and I.O. Murodullayev},
  journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
  year = {2026},
  volume = {1},
  number = {3},
  pages = {23-28},
  doi = {10.59251/2181-3973.2025.v1.138.1.3877},
  url = {https://doi.org/10.59251/2181-3973.2025.v1.138.1.3877}
}

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