Stochastic Diffusion-Convection Boundary Value Problems

The one dimensional diffusion-convection nonhomogeneous partial differential equation is solved under a stochastic source. The statistical moments of the solution process are obtained in closed form expressions for a general random source function. To illustrate the method of analysis, special cases are considered and an application concerning a pollution of a moving stream is introduced and solved numerically. Introducing the governing parameters, the statistical moments of the concentration of the pollutant is illustrated in terms of non-dimensional variables through figures.