Modeling of nonequilibrium cross-diffusion systems

In this research, we investigate the modeling of cross-diffusion systems that are not in equilibrium. For a particular equation, it is shown that the parameter values exist and have a numerical solution. A source describes the system of equations considered in this study as being based on the majority of physical processes, such as the cross-diffusion process in this system, thermal conductivity, and polytrophic filtration of gas and liquid in nonlinear media. Numerous partial solutions exist for these equations. The development of an integral self-similar solution is one of the most important approaches to analyzing the problem at hand. Initial construction of a system of self-similar equations using a nonlinear subtraction technique. The front for the equation of nonlinear heat generation with doubled energy was estimated, the localization process was observed, new effects were observed, an algorithm was constructed based on the obtained self-similar solution, a program code was developed in the programming language, and the process modeling was visualized.