TO THE PROPERTIES OF THE SOLUTIONS OF A NON-DIVERGENT NONLINEAR PARABOLIC SYSTEM DESCRIBING THE PROCESSES OF COMBUSTION
In this paper, the asymptotic behavior of self-similar solutions to the Cauchy problem for a system of
nonlinear parabolic equations in non-divergence form is obtained, and estimates for the subsolution
are derived.
1. Shu-Yu Hsu. Asymptotic behaviour of blow-up solutions of the fast diffusion equation. Nonlinear
Differential 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 Problems, 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. Explicit estimate for blow-up solutions of nonlinear parabolic systems
of non divergence form with variable density. Aip Conference Proceedings. 2023, 2781, 020055.
5. 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.
6. Aripov M. and Raimbekov J., “The critical curves of a doubly nonlinear parabolic equation in nondivergent
form with a source and nonlinear boundary flux,” Journal of Siberian Federal University 12(1),
2019, 112-124.
7. 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.
8. Aripov M., Atabaev O., Al-Marashi A. On the behavior of solutions of a doubly nonlinear degenerate
parabolic system with nonlinear sources and absorptions with variable densities. Bulletin of the Karaganda
University, 2025, No.1(117) pp. 12-23.
9. 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, pp. 57-67.
10. 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), pp. 1-7.
11. 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). 275-282.
12. Aripov M., Matyakubov A. S. Self-similar solutions of a cross-diffusion parabolic system with variable
density: explicit estimates and asymptotic behaviour. Nanosystems: Physics, Chemistry, Mathematics,
2017, 8(1), pp. 5-12.
13. Àðèïîâ Ì., Ñàäóëëàåâà Ñ. Êîìïüþòåðíîå ìîäåëèðîâàíèå íåëèíåéíûõ ïðîöåññîâ äèôôóçèè. Óíè-
âåðñèòåò, Òàøêåíò, 2020. 750 p.
14. Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A.P. Blow-up in Quasilinear Parabolic
Equations. Walter de Grueter, Berlin, 1995, 4, 535 p.
15. Aripov M., Sadullaeva S. A. Qualitative properties of solutions of a doubly nonlinear reaction-diffusion
system with a source. J Appl Math Phys, 2015. 3(9):1090-1099
16. Aripov M., Bobokandov M. M. Blow-up analysis for a doubly nonlinear parabolic non-divergence form
equation with source term. Bulletin of the Institute of Mathematics, 2022. Vol. 5, 4, ISSN-2181-9483.
17. Aripov M., Matyakubov A. S., Imomnazarov BK The Cauchy problem for a nonlinear degenerate
parabolic system in non-divergence form. Math Notes NEFU, 2020. 27(3):27-38
18. Aripov M., Matyakubov A. S., Xasanov J. O. Global solvability and explicit estimation of solutions of
a cross-di usion parabolic system in non-divergent form with a source and variable density. Bulletin of the
Institute of Mathematics, 2022, Vol. 5, 4, ISSN-2181-9483.
19. Rakhmonov Z. R., Khaydarov A., Urunbaev J. E. (2020) Global existence and nonexistence of solutions
to a cross diffusion system with nonlocal boundary conditions. Math Stat 8(4):404 409
20. Rakhmonov Z. R, Tillaev A. I. On the behavior of the solution of a nonlinear poly tropic filtration
problem with a source and multiple nonlinearities. Nanosyst Phys Chem Math, 2018. 9(3):323-329
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