Non-linear model of time-dependent relaxation cores for the systems with cross transfer effects

In this paper the non-linear generalization of model equations for relaxation cores with allowance for the influence of diffusion and heat relaxation times and cross transfer effects is submitted. It is proposed that physical interpretation of the non-linearity links to non-additive interaction invariants. The relaxation cores have been simulated in the form of expansion in power series of a small parameter having point of ratio between two Knudsen numbers calculated according to the characteristic space scales of elastic and inelastic molecules collisions, i.e. on Prigogine's approach. The time relaxation of temperature and concentration field's perturbations under the different values of small parameter has been calculated. It is established that non-linear interaction between temperature and concentration fields perturbations, initiated at different times, leads from some value of the small parameter to the phenomenon of the temporary increase of the perturbations.