Analytical Solution of ADE with Spatiotemporal Dependence of Dispersion Coefficient and Velocity using Green's Function Method

One dimensional advection diffusion equation (ADE) with variable coefficients is solved 
analytically using Green’s Function Method (GFM). ADE describes the pollutant mass transport 
in a heterogeneous medium originating from an instantaneous source. The heterogeneity of the 
medium is delineated through considering dispersion coefficient and velocity as functions of both 
the independent variables. The source term is defined by the non-homogeneous term in the ADE. 
A moving coordinate transformation is developed through which variable coefficients of the ADE 
are reduced into constant coefficients.