Nodivergent ko‘rinishdagi nochiziqli parabolik tenglama chegaralanmagan yechimlarini tadqiq etish
Nodivergent ko‘rinishdagi nochiziqli parabolik tenglama chegaralanmagan yechimlarini tadqiq etish
Keywords:
Nodivergent ko‘rinishdagi nochiziqli parabolikAbstract
Kirish. Amaliy matematikaning aktual yo‗nalishlaridan biri fizik jarayonlarning matematik
modellarini o‗rganishdan iboratdir. Ko‗pgina muhim masalalar chegaraviy shart ostida berilgan xususiy
hosilali chiziqsiz tenglamalar ko‘rinishida tasvirlanadi va ularning asosida matematik modellashtirish
yotadi. Nochiziqli masalalarni ba‘zi hollardagina analitik usulda yechish mumkin. Shu sababli ularni
taqribiy yechish usullaridan foydalangan holda yechimlar olinadi. Bunday usullar A.A. Samarskiy, A.S.
Kalashnikov [2], G.I. Barenblatt, P.O. Kershner, Y.B. Zeldovich [1], M.M.Aripov [8,9], Z.R. Rahmonov,
Sh.A. Sadullayeva, A.T. Xaydarov va boshqa olimlarning ishlarida keng yoritib berilgan.
References
Зельдович Я.Б., Компанеец А.С. К теории распространения тепла при теплопроводности, зависящей от температуры. Сборник, посвященный 70-летию акад. А. Ф. Иоффе. М. 1950, с.61-71.
Калашников А.С. О влиянии поглощения на распространение тепла в среде с теплопроводностью, зависящей от температуры. ЖВМ и МФ, 1976 т 16 № 3, с.689-696.
AS Matyakubov. Finite Speed of the Perturbation Distribution and Asymptotic Behavior of the Solutions of a Parabolic System not in Divergence Form. Universal Journal of Computational Mathematics 5 (3), 2017, 57-67.
AS Matyakubov, JO Khasanov, MO Ismoilova. Asymptotic representation of blow-up modes of parabolic equation not in divergence form with source. Сборник трудов I Международной научной конференции, 25-26 апреля 2022 года. Ташкент: Университет, 2022. С. 204-205.
AS Matyakubov, DR Raupov. Numerical and visual modeling for blow-up modes in two-component nonlinear media. Проблемы вычислительной и прикладной математики. Номер: 2 (39), 2022, Стр: 40-51.
AS Matyakubov, DR Raupov. Explicit estimate for blow-up solutions of nonlinear parabolic systems of non-divergence form with variable density. AIP Conference Proceedings, Volume 2781, Issue 1, 020055 (2023).
Matyakubov A. S., Raupov D. R. Estimates of the blow-up solution of a cross-diffusion parabolic system not in divergence form. Bukhara–Samarkand–Tashkent. – 2019. – Т. 16. – С. 106.
M Aripov, AS Matyakubov, JO Xasanov. Global solvability and explicit estimation of solutions of a cross-diffusion parabolic system in non-divergent form with a source and variable density. Mathematics and its application. Contemporary mathematics and its application: abstracts of the international scientific conference 2021, 23-24.
Mersaid A. et al. The Cauchy problem for a nonlinear degenerate parabolic system in non-divergence form. Математические заметки СВФУ. – 2020. – Т. 27. – №. 3. – С. 27-38.
