General solution to random advective-dispersive equation in porous media

Abstract

This series of articles present general applications of functional-analytic theory to the solution of the partial differential equation describing solid transport in aquifers, when either the evolution of the system, the sources, the parameters and/or the boundary conditions are prescribed as stochastic processes in time or in space. Part II of these series of articles completes the developments of part I by first presenting the semigroup solution of the randomly-forced three-dimensional advective-dispersive equation, and then introducing the semigroup solution for the particular case when the dispersion coefficient or the groundwater velocity are defined as stochastic processes in time or in space. As an illustration, the solution of the advective-dispersive equation subject to a time-stochastic dispersion coefficient is shown in detail. This new solution demonstrates that the time stochasticity in the dispersion coefficient may explain the uncertainly in the concentration distribution.