INVESTIGATION OF QUALITATIVE PROPERTIES OF THE NON-DIVERGENT CROSS-DIFFUSION PROBLEM WITH SOURCE AND VARIABLE DENSITY IN TWO-COMPONENT MEDIA IN CRITICAL CASES

Abstract

In this paper, we study the properties of self-similar solutions of a cross-diffusion parabolic system. The asymptotic behavior of self-similar solutions are analyzed for both the slow and fast diffusive regimes. It is shown that coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations.