Qualitative properties of the mathematical model of nonlinear cross-diffusion processes

The work is devoted to developing a self-similar solution for a system of nonlinear differential equations that describe diffusion processes. Various techniques are used to examine the capacity for generating self-similar solutions that can estimate and predict system behavior under diffusion conditions. The focus is on developing and applying numerical algorithms, as well as using theoretical tools such as asymptotic anal-ysis, to obtain more accurate and reliable results. The study’s results can be applied to various scientific and technical fields, such as physics, chemistry, biology, and engineering, where diffusion processes play an es-sential role. The development of self-similar solutions for systems of nonlinear differential equations related to diffusion opens novel opportunities for modeling and analyzing complex systems and enhancing diffusion processes in various fields.