Numerical Solution of the Multidimensional Cross-Diffusion Problem With Nonlinear Boundary Conditions

Key Points

• Asymptotic behavior of self-similar solutions was determined for a nonlinear cross-diffusion system, enhancing understanding of its implications.
• Numerical calculations show the effectiveness of using asymptotic formulas as initial approximations in iterative processes, providing robust approximations.
• An iterative process for selecting the initial approximation was proposed, aiding in the numerical solution for complex boundary conditions.
• Findings emphasize the importance of asymptotic behavior in understanding complex diffusion problems and improving numerical analysis techniques.