NOCHIZIQLI CHEGARAVIY SHARTLAR BILAN BERILGAN KOʻP OʻLCHAMLI KROSS-DIFFUZIYA MASALALARINING SONLI YECHIMLARI
Kalit so'zlar
https://doi.org/10.47390/ts-v3i10y2025No4Kalit so'zlar
kross-diffusiziya, nochiziqli chegaraviy shart, avtomodel.Annotasiya
Ushbu maqolada nochiziqli chegaraviy shartlarga ega boʻlgan nochiziqli kross-diffuziya sistemasining avtomodel yechimlarining asimptotik xatti-harakatlari oʻrganiladi. Avtomodel yechimlarning asimptotiklarining asosiy hadi aniqlandi. Koʻrib chiqilayotgan masalani sonli yechish uchun iterativ jarayonga mos keladigan boshlangʻich yaqinlashishni tanlash usuli taklif qilingan. Sonli hisob-kitoblar va natijalarni tahlil qilish iteratsiya jarayoni uchun boshlangʻich yaqinlashish sifatida asimptotik formulalar yordamida amalga oshirildi.
Manbalar
1. Tsiganov M.A., Biktashev V.N., Brindley J., Holden A.V., Ivanitsky G.R., Cross-diffusion waves in systems - a special class of nonlinear waves, UFN, 2007, Vol. 177, No. 3, 275-300.
2. Wu, Z.Q., Zhao, J.N., Yin, J.X. and Li, H.L., Nonlinear Diffusion Equations, Singapore: World Scientific, 2001.
3. Aripov M.M. Methods of basic equations for solving nonlinear boundary value problems. - Tashkent, Fan, 1988.
4. Kalashnikov A.S. Some problems of the qualitative theory of degenerate parabolic equations of the second order // UMN, Volume 42, Issue 2 (254), 1987, 135-176.
5. Murray J.D. Mathematical Biology, 3rd ed., Berlin: Springer, 2002-2003.
6. Malchow H, Petrovskii SV, Venturino E. Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models and Simulations. London: Chapman & Hall/CRC Press; 2008.
7. Levine, H., The Role of Critical Exponents in Blow-up Theorems, SIAM Rev., 32 (2), 1990, 262-288.
8. Wang S, Xie C H, Wang M X. Note on critical exponents for a system of heat equations with coupled boundary conditions. J Math Analysis Appl, 1998, 218: 313-324.
9. Wang S, Xie C H, Wang M X, Blow-up rate for a system of heat equations fully coupled in boundary conditions. Nonlinear Analysis, 1999, 35: 389-398.
10. Quiros F, Rossi J D. Blow-up set and Fujita-type curves for a nonlinear degenerate parabolic system with conditions. Indiana University Mathematics Journal, 2001, 50: 629-654.
11. Zheng S N, Song X F, Jiang Z X. Critical Fujita exponents for degenerate parabolic equations coupled by nonlinear boundary flux. J Math Analysis and Applications, 2004, 298: 308-324.
12. Rakhmonov Z.R., Urunbaev J.E. Numerical solution of the cross-diffusion problem with nonlocal boundary conditions // Problems of Computational and Applied Mathematics. 2019. - No. 4 (22). - pp. 88-100.
13. Rakhmonov Z.R., Urunbaev J.E. "On a Problem of Cross-Diffusion with Nonlocal Boundary Conditions," Journal of Siberian Federal University. Mathematics and Physics, no. 5, pp. 614-620. 2019, doi:10.17516/19971397-2019-12-5-614-620.
14. Rakhmonov Z.R., Khaydarov A., Urunbaev J.E., "Global Existence and Non-existence of Solutions to a Cross-Diffusion System with Nonlocal Boundary Conditions," Mathematics and Statistics, vol. 8, no. 4, pp. 404-409, 2020, doi:10.13189/ms.2020.080405.
15. Rakhmonov Z., Urunbaev J., and Alimov A., "Properties of Solutions of a System of Nonlinear Parabolic Equations with Nonlinear Boundary Conditions," AIP Conference Proc., vol. 2637, no. 1, pp. 040008-1-12, 2022. doi:10.1063/5.0119747
16. Rakhmonov Z., Alimov A., Urunbaev J. On the behavior of solutions for a system of multidimensional diffusion equationswith nonlinear boundary conditions // AIP Conference Proc., 2024, vol. 3085, no. 1, pp. 020032. https://doi.org/10.1063/5.0194896
17. Rakhmonov Z., Urunbaev E., Urunbaev J., Joniev A. On a problem of multidimensional cross-diffusion with nonlinear boundary conditions // International Journal of Applied Mathematics 2025 vol. 38 No. 1s, P. 987-996.
This work is licensed under a 