Abstract
Nolinear parabolik tenglamalar ko‘plab fizik, biologik va kimyoviy jarayonlarning matematik modelini ifodalaydi. Masalan, kimyoviy moddaning tarqalishi va reaktsiyasi, biologik populyatsiyalar evolyutsiyasi, issiqlik tarqalishi kabi. Ushbu maqolada o‘rganilayotgan tenglama quyidagicha
References
1. A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, A. P. Mikhailov, Blow-Up in Quasilinear Parabolic Equations, Walter de Gruyter, 1995.
2. J. M. Toshtemirov, "Effects of a multicomponent heat source on ambient density in multidimensional fields," ILM SARCHASHMALARI, 33-350, 2-son (fevral 2025).
3. J. M. Toshtemirov, " A mathematical model for convective and nonlinear heat transfer in multi-variable, multi-component media" ILM SARCHASHMALARI, 48-250, 5/2-son (may 2025).
4. Adrien Drouillet et al., "Multidimensional simulation of phase change by a D-2D model coupling via Stefan condition," Communications on Applied Mathematics and Computation, 2021.
5. M. M. Aripov, O. R. Djabbarov, Sh. Sadullaeva, "Mathematic modeling of processes describing by double nonlinear parabolic equation with convective transfer and damping," AIP Conference Proceedings, 2021.
6. A. T. Khaidarov, J. M. Toshtemirov, "Modeling of heat propagation processes in multidimensional domains," Modern Problems of Applied Mathematics and Information Technology, 2024.
7. A. T. Khaidarov, J. M. Toshtemirov, "Heat source density in non-linear heat dissipation processes," Proceedings of Scientific Conference on Multidisciplinary Studies, 2023.
8. A. Mamatov, J. Toshtemirov, "Visualization of the problem of multidimensional heat transfer through digital technologies," Pedagogical reforms and their solutions, 2024.
9. A. A. Samarskii, Teoriya raznostnyx sxem, Nauka, 1989.
10. U. U. Begulov, Kh. Abdugappor, J. M. Toshtemirov, "Cauchy problem for a parabolic equation describing the heat propagation process in a non-divergent form under the influence of an exponentially varying density," Matematik fizikaning zamonaviy usullari, 2025
