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Arxiv / №5.2 · 2026 / Maqola
01.00.00 – FIZIKA-MATEMATIKA FANLARI

YONISH JARAYONLARINI TAVSIFLOVCHI NODIVERGENT KO‘RINISHDAGI NOCHIZIQLI PARАBОLIK TENGLАMАLАR SISTEMASINING CHEGARALANMAGAN YЕCHIMLARINI BAHOLASH

Annotatsiya
O'ZBEKCHA

Ushbu maqolada yutilish va zichlikka ega nodivergent ko‘rinishdagi nochiziqli parаbо-lik tenglаmаlаr sistemasi uchun Koshi masalasi qaraladi, unga mos avtomodel tenglаmаlаr keltirib chiqa-rilgan hamda yuqori yеchim uchun baholar olingan.

Kalit so'zlar: matematik modellashtirish, avtomodel tahlil, parаbоlik tenglаmаlаr sistemasi, nodi-vergent shakl, yuqori yеchimlar.
РУССКИЙ

В данной работе рассматривается задача Коши для нелинейной параболической системы в недивергентной форме с поглощением и плотностью; выводятся соответствующие ав-томодельные уравнения, а также получены оценки для верхнего решения.

Ключевые слова: математическое моделирование, автомодельный анализ, cистема парабо-лических уравнений, недивергентная форма, верхнее решение.
ENGLISH

In this paper, the Cauchy problem for a nonlinear parabolic system in non-divergence form with absorption and density is considered, the corresponding self-similar equations are derived, and estimates for a supersolution are obtained.

Keywords: mathematical modeling, self-similar analysis, system of parabolic equations, non-diver-gence form, supersolution.
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Foydalanilgan adabiyotlar

  1. Shu-Yu Hsu. Asymptotic behaviour of blow-up solutions of the fast diffusion equation. Nonlinear Diffe-rential Equations and Applications NoDEA, 2023, p. 71–101.
  2. Yan Leng, Yuanyuan Nie, Qian Zhou. Asymptotic behavior of solutions to a class of coupled nonlinear parabolic systems. Boundary Value Pr., 2019, p. 68–79.
  3. Yohei Fujishima, Kazuhiro Ishige. Blowing Up Solutions for Nonlinear Parabolic Systems with Unequal Elliptic Operators. Dynamics and Differential Equations, 2019, p. 1219–1231.
  4. Matyakubov A.S., Raupov D.R. On Some Properties of the Blow-Up Solutions of a Nonlinear Parabolic System Non-divergent Form with Cross-Diffusion. Scopus: Springer Nature Switzerland AG. 2021, 289–303 p.
  5. Aripov M. and Raimbekov J. “The critical curves of a doubly nonlinear parabolic equation in non-divergent form with a source and nonlinear boundary flux,” Journal of Siberian Federal University 12(1), 2019, p. 112–124.
  6. Mirsaid Aripov, Alisher Matyakubov. To the qualitative properties of solution of system equations not in divergence form. International Journal of Innovative Science, Engineering Technology. 2016, p. 533–537
  7. Aripov M., Atabaev O., Al-Marashi A. On the behavior of solutions of a doubly nonlinear degenerate para-bolic system with nonlinear sources and absorptions with variable densities. Bulletin of the Karaganda Un-y, 2025, №.1 (117), p. 12–23.
  8. A.S.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, p. 57–67.
  9. Aripov M., Matyakubov A. To the properties of the solutions of a cross-diffusion parabolic system not in divergence form. Universal Journal of Computational Mathematics, 2017, 5(1), p. 1–7.
  10. Aripov M., Matyakubov A. On the asymptotic behavior solutions of nonlinear parabolic systems of equations not in divergence form. The KazNU Journal. 2015, 3 (86), p. 275–282.
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