About one problem of non-stationary convective transport with an initial distribution of a special type

The article is a study of the problem of hydrodynamic dispersion, including some types of mass transfer of a neutral indicator during the filtration of liquids. The purpose of the study is to determine the influence of the initial distribution on the mass transfer process and to identify the features of its dynamics. In the article, solutions to special cases of the Cauchy problem are obtained for some models that take into account the dissolution of substances. The authors note that the initial distribution of a special species can significantly change the transport dynamics and the formation of concentration gradients.