Convective heat conductivity and diffusion in one-dimensional hydrodynamics

Impurity concentration in the localized structures is described on the basis of the analytical solutions of the convective diffusion model equations in unidimensional hydrodynamic approach. In case of the Prandtl integral numbers, the solution of problems of nonstationary convective diffusion in the field of flow of evenly moving shock wave is boiled down to the solution of problems for heat conductivity equation. Relations between problems with integral-valued differences in the Prandtl numbers are determined. Various representations of the Green functions of the convective diffusion equations are analyzed. In case of the Prandtl integral numbers, they are expressed through the error integrals. The asymptotic nature of the solutions depends essentially on the observance of the integral laws of conservation. In case of the integral conservation of the impurity mass, the effect of coalescence of impurity solitons, their clusterization corresponds to the effect of coalescence of shock waves