O‘zbekiston matematika jurnali Volume 70 Issue 2 (2026) · pp. 187-198
Asymptotic Properties and Numerical Results of Solutions for a System of Degenerate Parabolic Equations with Nonlinear Boundary Conditions
Rakhmonov, Zafar, Zaripova, Aziza
Abstract
In this article, a system of parabolic equations with nonlinear boundary conditionsis transformed into a system of self-similar (automodel) equations by applying a shapeshifting. Anasymptotics for a compact supporting solution of the problem is proposed. The obtained asymptoticformulas are used as an initial approximation in the numerical solution of the problem. In numericalexperiments k = 3 is taken, a finite-difference scheme is proposed, and a Python program is developedto perform computations for various parameter values, corresponding graphs obtained.Numerical experiments have shown that the iterative processes converge within 3 to 5 steps. Thecompactly supported self-similar asymptotic solution used as the initial approximation played animportant role in ensuring the convergence of the iterative process. The graphs illustrate that, fordifferent numerical parameter values, the reaction–diffusion processes occur at a finite speed.
System of nonlinear equations,reaction-diffusionglobal solutionasymptoticnumer- ical solution.
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