Theory:: My doctoral work resolved a very general one-dimensional, linear partial-differential equation describing convective-diffusive or, equivalently, advective-dispersive behavior with sorption, desorption (a source), or decay. The problem was formulated for a finite domain with Robin (third-type) boundary conditions which, when transformed, yielded a system of ordinary differential equations with an eigenvalue expansion that composes a uniformly convergent series of real variables. As detailed in my dissertation, the one-dimensional transient solution I derive leads immediately and easily to a multi-dimensional solution (i.e., in two or three spatial dimensions). Then, the corresponding one-, two-, and three- dimensional steady-state problems are simply special cases thereof. Similarly, since the Robin (third-type) boundaries are composed as the sum of a Dirichlet (first-type) term and a Neumann (second-type) term, either of which can be identically zero, solutions for a first- or second-type boundary are furnished as a simple corollary, as discussed in an appendix to my dissertation.

Applications:: The general formulation chosen furnishes a solution for mass-transport in one-, two-, or three-dimensions. Problems may include sorption, desorption (a source), or decay (the solution remains valid when terms describing any of those phenomenon are identically zero). The furnished solution is valid for either first, second, or third-type boundary conditions. Physical problems may include surface- and ground- water pollution or the transport of therapeutic drugs across biofilm boundaries, cellular membranes, and venous walls. I will continue to respond to email inquiries from scientists whom need specific information regarding the way in which the solution may be adapted to a particular physical problem.