NUMERICAL SIMULATION OF A CROSS-DIFFUSION SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS AND DENSITY
DOI:
https://doi.org/10.47390/ts-v3i11y2025No1Keywords:
cross-diffusion, nonlinear boundary conditions, self-similar.Abstract
This paper examines the asymptotic behavior of self-similar solutions to a nonlinear cross-diffusion system with nonlocal boundary conditions and density. Various self-similar solutions to the problem for the case of slow diffusion are constructed, representing the asymptotic behavior of the solutions to the problem under consideration. The leading term of the asymptotic behavior of the self-similar solutions is obtained. For the numerical study of the problem under consideration, a method for selecting the optimal initial approximation for the iterative process is proposed. Numerical calculations are performed using asymptotic formulas as the initial approximation for the iterative process. The calculation results are visualized over time, and an analysis is provided.
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