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.
| Mualliflar | A. U. Mamatov, I.O. Murodullayev |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashr sanasi | 2026-07-01 |
| Jild | 1 |
| Son | 3 |
| Betlar | 23-28 |
| DOI | 10.59251/2181-3973.2025.v1.138.1.3877 |
DOI: 10.59251/2181-3973.2025.v1.138.1.3877 · Maqolaning asl sahifasi
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