Contribution of excesses of the highest order in the diffusion blurring concentration spots

Abstract

The paper develops a new ideology of solving the equations of mathematical physics, describing the molecular nature of the phenomenon. Owing to the nature of the problem to be solved the quasi-stationary probability density of a random variable, associated with the desired function, is introduced. The diffusion in an endless tube is considered as an example. The asymptotic behavior of the probability density of the diffusing particles is obtained coordinates study its statistical moments. Their evolution in time is set by the diffusion equation (without solutions) and the associated initial condition. It is shown how the error is associated with the excesses of the distribution function if the exact solution is replaced by its asymptotic expression.