Asymptotic theory of classical impurity transport in an inhomogeneous and non-stationary media. Hamilton’s formalism

An asymptotic theory of impurity transport in the diffusion-advection mode with the diffusivity and advection velocity slowly varying with coordinates and time is developed. The impurity concentration is reduced to single integral over time. The integrand is found from the solution of first-order ordinary differential equations, similar to Hamilton's equations for a material point in classical mechanics.