Numerical modeling of the cross diffusion process whith non-local boundary conditions

In this paper, we study the asymptotic behavior of self-similar solutions of nonlinear cross-diffusion system associated with nonlocal boundary conditions. We are constructed various self-similar solutions to the cross diffusion problem for the case of slow diffusion, which are the asymptotics of the solutions to the problem under consideration. The main term of the asymptotics of self-similar solutions is obtained. For a numerical study of the problem under consideration, a method is proposed for choosing the optimal initial approximation for the iterative process. Using asymptotic formulas as the initial approximation for the iterative process, numerical calculations are performed. The calculation results are visualized in time and the results are analyzed. Results of numerical experiments show that the obtained results are in good agreement with the physics of the process of nonlinear cross diffusion.

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