Analysis of a double nonlinear parabolic crosswise-diffusion system
Analysis of a double nonlinear parabolic crosswise-diffusion system
Keywords:
Keywords: Mandelbrot set, Julia set, bifurcation, fixed point, periodic point.Abstract
Annotation. Our main goal in this research is to investigate the characteristics of self-similar solutions to
the Cauchy problem. Specifically, we analyse the behaviour of these solutions in a source in a nonhomogenous
medium and in a double nonlinear time-dependent parabolic system of equations. We
investigate the self-similar analysis of the solutions, allowing us to establish the global solvability
conditions of the Cauchy problem of the Fujita type.
References
Aripov M.M., Djabbarov O.R. Method WKB for solutions of double nonlinear parabolic equation with damping term and variable coefficient, AIP Conference Proceedings 2781, 2023, 020018.
Aripov Mersaid and Makhmud Bobokandov. Asymptotic behavior of solutions for a doubly nonlinear parabolic non-divergence form equation with density. AIP Conference Proceedings, vol. 3004, no. 1. AIP Publishing, 2024.
Bobokandov Makhmud. Investigation of weak solutions of double nonlinear parabolic equation in nondivergence form with source term. Scientific Results 3, 2023.
Bobokandov Makhmud. Global solutions for double nonlinear parabolic crosswise-diffusion systems with time-dependent nonlinearity absorption. O‗zMU xabarlari 1/1, 2023.
Wang M. Some degenerate and quasilinear parabolic systems not in divergence form. J. Math. Anal. Appl., 2002, vol. 274, pp. 424–436.
Zhi-wen D., Li Zh. Global and blow-up solutions for nonlinear degenerate parabolic systems with crosswise-diffusion. Journal of Mathematical Analysis and Applications, 2000, vol. 244, pp. 263–278.
Арипов М.М., Садуллаева Ш.А. Компьютернное моделирование нелинейных процессов диффузии. Университет, Ташкент, 2020. 670 с.
