Numerical Modeling of Diffusion Processes in Two-Component Nonlinear Media with Variable Density and Source

In this work self-similar and approximately self-similar approach to the study of solutions of a double nonlinear parabolic system with a variable density and a source or absorption. The estimate of the weak solution, free boundary and the asymptotic behavior of the self-similar solution of the system for different cases studied. The qualitative properties of a solution of reaction-diffusion system and a double non-linearity with variable density established. Based it the problem of initial approximation solved, numerical analysis of the Cauchy problem for slowly diffusion, fast diffusion, critical and singular cases are analyzed.