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The evolution of the harmonic perturbation of one component of the stationary solution of the Carleman system is studied. The system can be used for mathematical modelling of technical problems in such fields: as the gas dynamics, the chemistry, acoustics etc. In particular, for the case of one dimensional space variable the system can be used to describe autokatalys problems for research of building materials. In this case the important property of the mathematical model is the stability of its stationary solutions. Numerical results of investigation of evolution perturbated stationary problem solution for special values of parameters are presented and analyze

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The investigation of evolution of the harmonic perturbation the stationary solution of the boundary value problem for a system of the Carleman equations