Cross-diffusion systems with convective transport

Abstract

The properties of cross-diffusion systems, which have double nonlinearity and include convective transfer, are investigated. This means that two factors are taken into account in the system: diffusion (random movement) and convection (transfer with the participation of the medium flow). The study of the properties of such systems makes it possible to understand how the interaction of these factors can influence the behavior of a population. The simulation of the processes of multicomponent cross-diffusion systems of a biological population with convective transfer on a computer is described. This means that with the help of numerical methods and computer models, models have been created that make it possible to simulate and study these systems. Such modeling helps to get an idea about the behavior of a cross-diffusion system under various conditions and system parameters. Estimates are obtained for solving the Cauchy problem of multicomponent cross-diffusion systems with convective transfer, which are analytical estimates of solutions. The study of the qualitative properties of the system made it possible to perform a numerical experiment depending on the values included in the system of numerical parameters.