The paper presents analytical solutions for 3D boundary value problems with time dependent parameters. Generally the problems considered describe diffusion and transport phenomena, but chemical reactions and other processes possibly accompanying the dispersion are also taken into account. The solutions are presented for 3D, 2D, and 1D flow domains with specific boundary conditions. In addition a relationship expressing the time evolution of the longitudinal dispersion coefficient and a method of analyzing its asymptotic behaviour at large time are deduced. The analytical results are used to interpret experimental breakthrough curves obtained from a natural gradient tracer experiment in an aquifer.