Analysis reveals the asymptotic behavior of self-similar solutions in a nonlinear cross-diffusion system, suggesting improvements in numerical calculations.
This article investigates the asymptotic behavior of self-similar solutions of a nonlinear cross-diffusion system with nonlocal boundary conditions. The main term of the asymptotics of self-similar solutions has been determined. For the numerical study of the problem under consideration, a method for selecting the initial approximation corresponding to the iterative process is proposed. Numerical calculations and analysis of the results were carried out using asymptotic formulas as an initial approximation for the iteration process.
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Rakhmonov et al. (2025) studied this question.
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