On the properties of the solutions of the problem of cross-diffusion with the dual nonlinearity and the convective transfer

Abstract

Abstract In this work, special methods for studying nonlinear parabolic equations were developed that allow a fairly detailed study of nonlinear problems based on self-similar and approximately self-similar solutions and the construction of an analogue Zeldovych-Kompanees type solution for a cross system, since the study of self-similar equations is relatively simpler in comparison with equations in private derivatives. Studied the properties of solutions to the problem of a biological population of the Fisher-Kolmogorov type in the case of cross-diffusion with the dual nonlinearity and the convective transfer. An estimate of the solutions is obtained, and on the basis of it the problem of choosing the initial approximation for the numerical solution of the Cauchy problem is solved.