We study a one-dimensional model of transport of a chemical tracer in a porous media with fracture zones. The medium is modeled by porous blocks separated by fracture channels that conduct water via advection and dispersion; the channels communicate with each other by diffusion. We obtain an analytic solution in the case of periodic Dirichlet and periodic flux- type (Robin) boundary conditions.
Logan, J. D., Zlotnik, V. A., & Cohn, S. (1996). Transport in fractured porous media with time-periodic boundary conditions. Mathematical and Computer Modelling, 24(9), 1–9. https://doi.org/10.1016/0895-7177(96)00149-5