NODIVERGENT TURIDAGI O‘ZGARUVCHAN ZICHLIKKA EGA KROSS-DIFFUZIYA SISTEMASINING AVTOMODEL YECHIMI VA SONLI YAQINLASHTIRISH.
Keywords:
Kross-diffuziya, avtomodel yechimlar, sonli yechimlar, iteratsiya, chiziqlilashtirish, iterativ Picard metodi.Abstract
Ushbu maqolada nodivergent turdagi chiziqsiz parabolik kross-diffuziya tenglamalari sistemasini bir xil bo‘lmagan tarqalish muhitlarida sonli yechishni ko‘rib chiqamiz. Ishning asosiy maqsadi bu boshlang‘ich va chegaraviy shartlarni qanoatlantiradigan taqribiy yechimni qurib olish va uni tenglamani barcha shartlarini qanoatlantirishini taminlashdan iborat. Bu bilan birgalikda sistema uchun sonli yechimlar jadvalini iteratsion jarayonlardan foydalangan holda qurish.
References
Wu, Z.Q., Zhao, J.N., Yin, J.X. and Li, H.L., Nonlinear Diffusion Equations, Singapore: World Scientific, 2001.
Арипов М.М. Методы эталонных уравнений для решения нелинейных краевых задач. - Ташкент, Фан, 1988.
Murray J.D. Mathematical Biology, 3rd ed., Berlin: Springer, 2002-2003.
Malchow H, Petrovskii SV, Venturino E. Spatiotemporal patterns in ecology and epidemiology: theory, models, and simulations. London: Chapman & Hall/CRC Press; 2008.
M.A. Tsyganov, V.N. Biktashev, J. Brindley, A.V. Holden, G.R. Ivanitsky, Waves in cross-diffusion systems – a special class of nonlinear waves, UFN, 2007, vol. 177, issue 3, 275-300.
Levine, H., The role of critical exponents in blowup theorems, SIAM Rev., 32(2), 1990, 262-288.
Wang S, Xie C H, Wang M X. Note on critical exponents for a system of heat equations coupled in the boundary conditions. J Math Analysis Applic, 1998, 218: 313–324.
Wang S, Xie C H, Wang M X, The blow-up rate for a system of heat equations completely coupled in the boundary conditions. Nonlinear Anal, 1999, 35: 389–398.
Quiros F, Rossi J D. Blow-up set and Fujita-type curves for a degenerate parabolic system with nonlinear conditions. Indiana Univ Math J, 2001, 50: 629–654.
Zheng S N, Song X F, Jiang Z X. Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux. J Math Anal Appl, 2004, 298: 308–324.
Aripov M.M., Matyakubov A.S. Self-similar solutions of a cross-diffusion parabolic system with variable density: explicit estimates and asymptotic behavior. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8(1), 5-12.
Z. R. Rakhmonov, J. E. Urunbaev and A. A. Alimov Properties of solutions of a system of nonlinear parabolic equations with nonlinearboundary conditions AIP Conference Proceedings 2637, 040008 (2022);
7. Aripov M., Rakhmonov Z. (2016). On the behavior of the solution of a nonlinear multidimensional polytropic filtration problem with a variable coefficient and nonlocal boundary condition. Contemporary Analysis and Applied Mathematics, Vol. 4, № 1, 23-32.
Yarmetova D.I., Nazirova D.X. NUMERICAL SOLUTIONS OF NONLINEAR CROSS DIFFUSION SYSTEMS WITH VARIABLE DENSITY,2022
З.Р.Рахмоно,Ж.Э.Урунбае, Д.И.Ярметов Численное решение задачи кросс диффузии с нелокальными граничными условиями и переменной плотностью ,Scientific journal,2022,28-39
