Response functions of the convection-dispersion equations describing radionuclide migration in a semi-infinite medium

Analytic expressions are derived for the response functions for the set of n coupled convection-dispersion equations in 1-D and with constant coefficients, for an n-member radioactive decay chain. The one-sided Laplace transform is applied to this set of partial differential equations, and eigen vectors and eigen values of the resulting system of equations are used to obtain general expressions for the Laplace transforms of the response functions. These are then inverted to produce analytic expressions for the response functions. These are used to solve problems with arbitrary time-varying boundary condition using convolutions. Laplace transforms of systems having similar characteristics can be written readily using results presented in this paper.