  We study the existence and uniqueness of a solution to a linear stationary
convection-diffusion equation stated in an infinite cylinder, Neumann boundary
condition being imposed on the boundary. We assume that the cylinder is a
junction of two semi-infinite cylinders with two different periodic regimes.
Depending on the direction of the effective convection in the two semi-infinite
cylinders, we either get a unique solution, or one-parameter family of
solutions, or even non-existence in the general case. In the latter case we
provide necessary and sufficient conditions for the existence of a solution.
