Numerical investigation of some stationary solutions of the Carleman system

Abstract

Abstract. The negative stationary solutions of the boundary value problem for the Carleman system of equations are investigated. The kinetic Carleman system is a system of two nonlinear partial differential equations. The system describes the interaction of transportation and nonlinear processes. So, it is used for mathematical modelling of problems in various fields: the kinetic theory of gasses, the gas dynamics, the chemistry, ecology, acoustics etc. In particular, the system can be used to describe autokatalys problems for research of building materials. We present and discuss results of numerical investigation of negative problem solution for different values of parameters. There are three problem parameters domains. For the first parameters domain the stationary solution has stable character, for the second parameters domain the stationary solution has stochastic character and for third domain the stationary solution has unstable character.