WIT Press


A Stochastic Approach To The Diffusion Equation

Price

Free (open access)

Paper DOI

10.2495/AIR010121

Volume

47

Pages

9

Published

2001

Size

598 kb

Author(s)

B. Spagnolo & P. Barrera

Abstract

We propose a stochastic differential equation for the pollutant concentra- tion. This equation models the advection-diffusion equation of air pollution in the atmosphere. We obtain exact solution for the mean concentration and its standard deviation in three dimensional case. We give also the general expression of the higher moments of th^ concentration. As particular cases we obtain the exact steady state solution for neutral atmosphere conditions and for weak wind. 1 Introduction The dispersion of pollutants in the atmosphere is usually described by the diffusion equation which reads [1] c)c & c9c r/c 0 / cVc\ ^ /^ ^^A , ^ ^ ^^ /i —+ ^. — 4-r —4-^;— ^ — Dr

Keywords